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Journal articles on the topic 'Neural oscillators'

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Published: 4 June 2021

Last updated: 16 February 2022

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BONNIN, MICHELE, FERNANDO CORINTO, and MARCO GILLI. "BIFURCATIONS, STABILITY AND SYNCHRONIZATION IN DELAYED OSCILLATORY NETWORKS." International Journal of Bifurcation and Chaos 17, no. 11 (2007): 4033–48. http://dx.doi.org/10.1142/s0218127407019846.

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Current studies in neurophysiology award a key role to collective behaviors in both neural information and image processing. This fact suggests to exploit phase locking and frequency entrainment in oscillatory neural networks for computational purposes. In the practical implementation of artificial neural networks delays are always present due to the non-null processing time and the finite signal propagation speed. This manuscript deals with networks composed by delayed oscillators, we show that either long delays or constant external inputs can elicit oscillatory behavior in the single neural oscillator. Using center manifold reduction and normal form theory, the equations governing the whole network dynamics are reduced to an amplitude-phase model (i.e. equations describing the evolution of both the amplitudes and the phases of the oscillators). The analysis of a network with a simple architecture reveals that different kind of phase locked oscillations are admissible, and the possible coexistence of in-phase and anti-phase locked solutions.

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HUANG, WEIWEI, CHEE-MENG CHEW, YU ZHENG, and GEOK-SOON HONG. "BIO-INSPIRED LOCOMOTION CONTROL WITH COORDINATION BETWEEN NEURAL OSCILLATORS." International Journal of Humanoid Robotics 06, no. 04 (2009): 585–608. http://dx.doi.org/10.1142/s0219843609001929.

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Central Pattern Generator (CPG) is used in bipedal locomotion control to provide the basic rhythm signal for actuators. Generally, the CPG is composed of many neural oscillators coupled together. In this paper, the coordination between neural oscillators in CPG is studied to achieve robust rhythm motions. By using the entrainment property of the neural oscillator, we develop a method which uses the difference between oscillator's output and desired output to adjust the inner states of neural oscillators. In the simulation, a CPG structure with coordination between neural oscillators is used to control a 2D bipedal robot. The robot can walk continuously when several external forces are applied on the robot during walking. The method is also implemented on our humanoid robot NUSBIP-III ASLAN for the test of walking forward. With the coordination between neural oscillators, the CPG generated rhythmic and robust control signals which enable the robot to walk forward stably.

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Horn, David, and Irit Opher. "Temporal Segmentation in a Neural Dynamic System." Neural Computation 8, no. 2 (1996): 373–89. http://dx.doi.org/10.1162/neco.1996.8.2.373.

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Oscillatory attractor neural networks can perform temporal segmentation, i.e., separate the joint inputs they receive, through the formation of staggered oscillations. This property, which may be basic to many perceptual functions, is investigated here in the context of a symmetric dynamic system. The fully segmented mode is one type of limit cycle that this system can develop. It can be sustained for only a limited number n of oscillators. This limitation to a small number of segments is a basic phenomenon in such systems. Within our model we can explain it in terms of the limited range of narrow subharmonic solutions of the single nonlinear oscillator. Moreover, this point of view allows us to understand the dominance of three leading amplitudes in solutions of partial segmentation, which are obtained for high n. The latter are also abundant when we replace the common input with a graded one, allowing for different inputs to different oscillators. Switching to an input with fluctuating components, we obtain segmentation dominance for small systems and quite irregular waveforms for large systems.

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Wang, DeLiang L. "On Connectedness: A Solution Based on Oscillatory Correlation." Neural Computation 12, no. 1 (2000): 131–39. http://dx.doi.org/10.1162/089976600300015916.

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A long-standing problem in neural computation has been the problem of connectedness, first identified by Minsky and Papert (1969). This problem served as the cornerstone for them to establish analytically that perceptrons are fundamentally limited in computing geometrical (topological) properties. A solution to this problem is offered by a different class of neural networks: oscillator networks. To solve the problem, the representation of oscillatory correlation is employed, whereby one pattern is represented as a synchronized block of oscillators and different patterns are represented by distinct blocks that desynchronize from each other. Oscillatory correlation emerges from LEGION (locally excitatory globally inhibitory oscillator network), whose architecture consists of local excitation and global inhibition among neural oscillators. It is further shown that these oscillator networks exhibit sensitivity to topological structure, which may lay a neurocomputational foundation for explaining the psychophysical phenomenon of topological perception.

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Oprisan, Sorinel A. "All Phase Resetting Curves Are Bimodal, but Some Are More Bimodal Than Others." ISRN Computational Biology 2013 (December 12, 2013): 1–11. http://dx.doi.org/10.1155/2013/230571.

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Phase resetting curves (PRCs) are phenomenological and quantitative tools that tabulate the transient changes in the firing period of endogenous neural oscillators as a result of external stimuli, for example, presynaptic inputs. A brief current perturbation can produce either a delay (positive phase resetting) or an advance (negative phase resetting) of the subsequent spike, depending on the timing of the stimulus. We showed that any planar neural oscillator has two remarkable points, which we called neutral points, where brief current perturbations produce no phase resetting and where the PRC flips its sign. Since there are only two neutral points, all PRCs of planar neural oscillators are bimodal. The degree of bimodality of a PRC, that is, the ratio between the amplitudes of the delay and advance lobes of a PRC, can be smoothly adjusted when the bifurcation scenario leading to stable oscillatory behavior combines a saddle node of invariant circle (SNIC) and an Andronov-Hopf bifurcation (HB).

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McDowell, Patrick, and Theresa Beaubouef. "Neural Oscillators Programming Simplified." Applied Computational Intelligence and Soft Computing 2012 (2012): 1–9. http://dx.doi.org/10.1155/2012/963917.

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The neurological mechanism used for generating rhythmic patterns for functions such as swallowing, walking, and chewing has been modeled computationally by the neural oscillator. It has been widely studied by biologists to model various aspects of organisms and by computer scientists and robotics engineers as a method for controlling and coordinating the gaits of walking robots. Although there has been significant study in this area, it is difficult to find basic guidelines for programming neural oscillators. In this paper, the authors approach neural oscillators from a programmer’s point of view, providing background and examples for developing neural oscillators to generate rhythmic patterns that can be used in biological modeling and robotics applications.

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Velichko, Andrey, Maksim Belyaev, Vadim Putrolaynen, Alexander Pergament, and Valentin Perminov. "Switching dynamics of single and coupled VO2-based oscillators as elements of neural networks." International Journal of Modern Physics B 31, no. 02 (2017): 1650261. http://dx.doi.org/10.1142/s0217979216502611.

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In the present paper, we report on the switching dynamics of both single and coupled VO2-based oscillators, with resistive and capacitive coupling, and explore the capability of their application in oscillatory neural networks. Based on these results, we further select an adequate SPICE model to describe the modes of operation of coupled oscillator circuits. Physical mechanisms influencing the time of forward and reverse electrical switching, that determine the applicability limits of the proposed model, are identified. For the resistive coupling, it is shown that synchronization takes place at a certain value of the coupling resistance, though it is unstable and a synchronization failure occurs periodically. For the capacitive coupling, two synchronization modes, with weak and strong coupling, are found. The transition between these modes is accompanied by chaotic oscillations. A decrease in the width of the spectrum harmonics in the weak-coupling mode, and its increase in the strong-coupling one, is detected. The dependences of frequencies and phase differences of the coupled oscillatory circuits on the coupling capacitance are found. Examples of operation of coupled VO2 oscillators as a central pattern generator are demonstrated.

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Velichko. "A Method for Evaluating Chimeric Synchronization of Coupled Oscillators and Its Application for Creating a Neural Network Information Converter." Electronics 8, no. 7 (2019): 756. http://dx.doi.org/10.3390/electronics8070756.

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This paper presents a new method for evaluating the synchronization of quasi-periodic oscillations of two oscillators, termed “chimeric synchronization”. The family of metrics is proposed to create a neural network information converter based on a network of pulsed oscillators. In addition to transforming input information from digital to analogue, the converter can perform information processing after training the network by selecting control parameters. In the proposed neural network scheme, the data arrives at the input layer in the form of current levels of the oscillators and is converted into a set of non-repeating states of the chimeric synchronization of the output oscillator. By modelling a thermally coupled VO2-oscillator circuit, the network setup is demonstrated through the selection of coupling strength, power supply levels, and the synchronization efficiency parameter. The distribution of solutions depending on the operating mode of the oscillators, sub-threshold mode, or generation mode are revealed. Technological approaches for the implementation of a neural network information converter are proposed, and examples of its application for image filtering are demonstrated. The proposed method helps to significantly expand the capabilities of neuromorphic and logical devices based on synchronization effects.

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Fukai, Tomoki, and Masatoshi Shiino. "Memory Recall by Quasi-Fixed-Point Attractors in Oscillator Neural Networks." Neural Computation 7, no. 3 (1995): 529–48. http://dx.doi.org/10.1162/neco.1995.7.3.529.

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It is shown that approximate fixed-point attractors rather than synchronized oscillations can be employed by a wide class of neural networks of oscillators to achieve an associative memory recall. This computational ability of oscillator neural networks is ensured by the fact that reduced dynamic equations for phase variables in general involve two terms that can be respectively responsible for the emergence of synchronization and cessation of oscillations. Thus the cessation occurs in memory retrieval if the corresponding term dominates in the dynamic equations. A bottomless feature of the energy function for such a system makes the retrieval states quasi-fixed points, which admit continual rotating motion to a small portion of oscillators, when an extensive number of memory patterns are embedded. An approximate theory based on the self-consistent signal-to-noise analysis enables one to study the equilibrium properties of the neural network of phase variables with the quasi-fixed-point attractors. As far as the memory retrieval by the quasi-fixed points is concerned, the equilibrium properties including the storage capacity of oscillator neural networks are proved to be similar to those of the Hopfield type neural networks.

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Hayashi, Yukio. "Numerical Bifurcation Analysis of an Oscillatory Neural Network with Synchronous/Asynchronous Connections." Neural Computation 6, no. 4 (1994): 658–67. http://dx.doi.org/10.1162/neco.1994.6.4.658.

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One of the advantages of oscillatory neural networks is their dynamic links among related features; the links are based on input-dependent synchronized oscillations. This paper investigates the relations between synchronous/asynchronous oscillations and the connection architectures of an oscillatory neural network with two excitatory-inhibitory pair oscillators. Through numerical analysis, we show synchronous and asynchronous connection types over a wide parameter space for two different inputs and one connection parameter. The results are not only consistent with the classification of synchronous/asynchronous connection types in König's model (1991), but also offer a useful guideline on how to construct a network with local connections for a segmentation task.

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Han, Seung Kee, Seon Hee Park, Tae Gyu Yim, Seunghwan Kim, and Seunghwan Kim. "Chaotic Bursting Behavior of Coupled Neural Oscillators." International Journal of Bifurcation and Chaos 07, no. 04 (1997): 877–88. http://dx.doi.org/10.1142/s0218127497000674.

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Recently it was shown that dephasing of diffusively coupled neural oscillators leads to a new class of bursting phenomena, where neural oscillators switch between high and low oscillation amplitudes. To analyze this behavior we study a system of three-coupled neurons, which is the most simple one that shows chaotic bursting behavior. For the intermediate values of coupling constant kc, the chaotic bursting behavior occurs. For a quantitative analysis of chaotic bursting, we introduce three mean activities of oscillators. From the Poincaré sections we find a period-doubling route to chaos. We illustrate the busting behavior in terms of competition of the single oscillator behavior with the collective one arising from the diffusive coupling of oscillators.

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Moriyama, Takuro, and Daisuke Kurabayashi. "Adaptive Control Using an Oscillator Network with Capacitive Couplers." Journal of Advanced Computational Intelligence and Intelligent Informatics 15, no. 6 (2011): 632–38. http://dx.doi.org/10.20965/jaciii.2011.p0632.

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We focus on the oscillatory aspects of neural components and their roles in neural system functionality such as adaptability. This study provides an implementation of adaptive control by using a network system consisting of oscillators and capacitive couplers. The functionality of oscillators alone is fairly limited, but capacitive couplers change interaction between oscillators, enabling logical operations, absolute function, gain variable amplifiers, and adaptive control. We provide basic functional networks of oscillators and capacitive couplers and demonstrate adaptive control implementation based on these functions.

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Jeong, Ho Young, and Boris Gutkin. "Synchrony of Neuronal Oscillations Controlled by GABAergic Reversal Potentials." Neural Computation 19, no. 3 (2007): 706–29. http://dx.doi.org/10.1162/neco.2007.19.3.706.

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GABAergic synapse reversal potential is controlled by the concentration of chloride. This concentration can change significantly during development and as a function of neuronal activity. Thus, GABA inhibition can be hyperpolarizing, shunting, or partially depolarizing. Previous results pinpointed the conditions under which hyperpolarizing inhibition (or depolarizing excitation) can lead to synchrony of neural oscillators. Here we examine the role of the GABAergic reversal potential in generation of synchronous oscillations in circuits of neural oscillators. Using weakly coupled oscillator analysis, we show when shunting and partially depolarizing inhibition can produce synchrony, asynchrony, and coexistence of the two. In particular, we show that this depends critically on such factors as the firing rate, the speed of the synapse, spike frequency adaptation, and, most important, the dynamics of spike generation (type I versus type II). We back up our analysis with simulations of small circuits of conductance-based neurons, as well as large-scale networks of neural oscillators. The simulation results are compatible with the analysis: for example, when bistability is predicted analytically, the large-scale network shows clustered states.

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Wilson, Hugh R. "Hyperchaos in Wilson–Cowan oscillator circuits." Journal of Neurophysiology 122, no. 6 (2019): 2449–57. http://dx.doi.org/10.1152/jn.00323.2019.

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The Wilson–Cowan equations were originally shown to produce limit cycle oscillations for a range of parameters. Others subsequently showed that two coupled Wilson–Cowan oscillators could produce chaos, especially if the oscillator coupling was from inhibitory interneurons of one oscillator to excitatory neurons of the other. Here this is extended to show that chains, grids, and sparse networks of Wilson–Cowan oscillators generate hyperchaos with linearly increasing complexity as the number of oscillators increases. As there is now evidence that humans can voluntarily generate hyperchaotic visuomotor sequences, these results are particularly relevant to the unpredictability of a range of human behaviors. These also include incipient senescence in aging, effects of concussive brain injuries, autism, and perhaps also intelligence and creativity. NEW & NOTEWORTHY This paper represents an exploration of hyperchaos in coupled Wilson–Cowan equations. Results show that hyperchaos (number of positive Lyapunov exponents) grows linearly with the number of oscillators in the array and leads to high levels of unpredictability in the neural response.

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UETA, TETSUSHI, and HIROSHI KAWAKAMI. "BIFURCATION IN ASYMMETRICALLY COUPLED BVP OSCILLATORS." International Journal of Bifurcation and Chaos 13, no. 05 (2003): 1319–27. http://dx.doi.org/10.1142/s0218127403007199.

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BVP oscillator is the simplest mathematical model describing dynamical behavior of neural activity. Large scale neural network can often be described naturally by coupled systems of BVP oscillators. However, even if two BVP oscillators are merely coupled by a linear element, the whole system exhibits complicated behavior. In this letter, we analyze coupled BVP oscillators with asymmetrical coupling structure, besides, each oscillator has different internal resistance. The system shows a rich variety of bifurcation phenomena and strange attractors. We calculate bifurcation diagrams in two-parameter plane around which the chaotic attractors mainly appear and confirm relaxant phenomena in the laboratory experiments. We also briefly report a conspicuous strange attractor.

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Hattori, Yuya, Michiyo Suzuki, Zu Soh, Yasuhiko Kobayashi, and Toshio Tsuji. "Theoretical and Evolutionary Parameter Tuning of Neural Oscillators with a Double-Chain Structure for Generating Rhythmic Signals." Neural Computation 24, no. 3 (2012): 635–75. http://dx.doi.org/10.1162/neco_a_00249.

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A neural oscillator with a double-chain structure is one of the central pattern generator models used to simulate and understand rhythmic movements in living organisms. However, it is difficult to reproduce desired rhythmic signals by tuning an enormous number of parameters of neural oscillators. In this study, we propose an automatic tuning method consisting of two parts. The first involves tuning rules for both the time constants and the amplitude of the oscillatory outputs based on theoretical analyses of the relationship between parameters and outputs of the neural oscillators. The second involves an evolutionary tuning method with a two-step genetic algorithm (GA), consisting of a global GA and a local GA, for tuning parameters such as neural connection weights that have no exact tuning rule. Using numerical experiments, we confirmed that the proposed tuning method could successfully tune all parameters and generate sinusoidal waves. The tuning performance of the proposed method was less affected by factors such as the number of excitatory oscillators or the desired outputs. Furthermore, the proposed method was applied to the parameter-tuning problem of some types of artificial and biological wave reproduction and yielded optimal parameter values that generated complex rhythmic signals in Caenorhabditis elegans without trial and error.

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Ermentrout, G. B., and N. Kopell. "Oscillator Death in Systems of Coupled Neural Oscillators." SIAM Journal on Applied Mathematics 50, no. 1 (1990): 125–46. http://dx.doi.org/10.1137/0150009.

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Endo, Tetsuro, and Kazuhiro Takeyama. "Neural network using oscillators." Electronics and Communications in Japan (Part III: Fundamental Electronic Science) 75, no. 5 (1992): 51–59. http://dx.doi.org/10.1002/ecjc.4430750505.

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Yang, Woosung, Jaesung Kwon, Nak Young Chong, and Yonghwan Oh. "Biologically Inspired Robotic Arm Control Using an Artificial Neural Oscillator." Mathematical Problems in Engineering 2010 (2010): 1–16. http://dx.doi.org/10.1155/2010/107538.

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We address a neural-oscillator-based control scheme to achieve biologically inspired motion generation. In general, it is known that humans or animals exhibit novel adaptive behaviors regardless of their kinematic configurations against unexpected disturbances or environment changes. This is caused by the entrainment property of the neural oscillator which plays a key role to adapt their nervous system to the natural frequency of the interacted environments. Thus we focus on a self-adapting robot arm control to attain natural adaptive motions as a controller employing neural oscillators. To demonstrate the excellence of entrainment, we implement the proposed control scheme to a single pendulum coupled with the neural oscillator in simulation and experiment. Then this work shows the performance of the robot arm coupled to neural oscillators through various tasks that the arm traces a trajectory. With these, the real-time closed-loop system allowing sensory feedback of the neural oscillator for the entrainment property is proposed. In particular, we verify an impressive capability of biologically inspired self-adaptation behaviors that enables the robot arm to make adaptive motions corresponding to an unexpected environmental variety.

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Campbell, Shannon R., DeLiang L. Wang, and Ciriyam Jayaprakash. "Synchrony and Desynchrony in Integrate-and-Fire Oscillators." Neural Computation 11, no. 7 (1999): 1595–619. http://dx.doi.org/10.1162/089976699300016160.

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Due to many experimental reports of synchronous neural activity in the brain, there is much interest in understanding synchronization in networks of neural oscillators and its potential for computing perceptual organization. Contrary to Hopfield and Herz (1995), we find that networks of locally coupled integrate-and-fire oscillators can quickly synchronize. Furthermore, we examine the time needed to synchronize such networks. We observe that these networks synchronize at times proportional to the logarithm of their size, and we give the parameters used to control the rate of synchronization. Inspired by locally excitatory globally inhibitory oscillator network (LEGION) dynamics with relaxation oscillators (Terman & Wang, 1995), we find that global inhibition can play a similar role of desynchronization in a network of integrate-and-fire oscillators. We illustrate that a LEGION architecture with integrate-and-fire oscillators can be similarly used to address image analysis.

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Orchard, Jeff. "Oscillator-Interference Models of Path Integration Do Not Require Theta Oscillations." Neural Computation 27, no. 3 (2015): 548–60. http://dx.doi.org/10.1162/neco_a_00701.

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Navigation and path integration in rodents seems to involve place cells, grid cells, and theta oscillations (4–12 Hz) in the local field potential. Two main theories have been proposed to explain the neurological underpinnings of how these phenomena relate to navigation and to each other. Attractor network (AN) models revolve around the idea that local excitation and long-range inhibition connectivity can spontaneously generate grid-cell-like activity patterns. Oscillator interference (OI) models propose that spatial patterns of activity are caused by the interference patterns between neural oscillators. In rats, these oscillators have a frequency close to the theta frequency. Recent studies have shown that bats do not exhibit a theta cycle when they crawl, and yet they still have grid cells. This has been interpreted as a criticism of OI models. However, OI models do not require theta oscillations. We explain why the absence of theta oscillations does not contradict OI models and discuss how the two families of models might be distinguished experimentally.

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Granada, Adrián E., Trinitat Cambras, Antoni Díez-Noguera, and Hanspeter Herzel. "Circadian desynchronization." Interface Focus 1, no. 1 (2010): 153–66. http://dx.doi.org/10.1098/rsfs.2010.0002.

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The suprachiasmatic nucleus (SCN) coordinates via multiple outputs physiological and behavioural circadian rhythms. The SCN is composed of a heterogeneous network of coupled oscillators that entrain to the daily light–dark cycles. Outside the physiological entrainment range, rich locomotor patterns of desynchronized rhythms are observed. Previous studies interpreted these results as the output of different SCN neural subpopulations. We find, however, that even a single periodically driven oscillator can induce such complex desynchronized locomotor patterns. Using signal analysis, we show how the observed patterns can be consistently clustered into two generic oscillatory interaction groups: modulation and superposition. In seven of 17 rats undergoing forced desynchronization, we find a theoretically predicted third spectral component. Combining signal analysis with the theory of coupled oscillators, we provide a framework for the study of circadian desynchronization.

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ZHANG, DINGGUO, and KUANYI ZHU. "THEORETICAL ANALYSIS ON NEURAL OSCILLATOR TOWARD BIOMIMIC ROBOT CONTROL." International Journal of Humanoid Robotics 04, no. 04 (2007): 697–715. http://dx.doi.org/10.1142/s0219843607001229.

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Neural oscillator is derived from the central pattern generator (CPG) in the biological nervous system. It can generate motor patterns for the rhythmic movements. Neural oscillator is widely adopted in biomimic robot and humanoid robot for different types of rhythmic movement controls such as swimming and walking. Theoretical analysis about neural oscillator toward biomimic robot control is presented in this paper. The methods adopted here include stability theory, describing function, and piecewise linear analysis. Some important properties of the neural oscillator, such as the determination of frequency, oscillation, and stability, are exploited. Network property of multiple neural oscillators is also studied. The insightful results will strengthen the foundation of the neural oscillator and enhance its efficient application for robotic control purpose.

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LANZA, VALENTINA, LINDA PONTA, MICHELE BONNIN, and FERNANDO CORINTO. "MULTIPLE ATTRACTORS AND BIFURCATIONS IN HARD OSCILLATORS DRIVEN BY CONSTANT INPUTS." International Journal of Bifurcation and Chaos 22, no. 11 (2012): 1250267. http://dx.doi.org/10.1142/s0218127412502677.

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Hard oscillators are dynamical systems that show the coexistence of qualitatively different attractors, in the form of limit cycles and equilibrium points. In the presence of external inputs their dynamic behavior is significantly different from those of oscillators, called soft, with a limit cycle as unique attractor. This paper studies the dynamics of a simple hard oscillator under the influence of a constant external input. It is shown that, despite the apparent simplicity, when the input strength and the oscillator's natural frequency are varied the system exhibits many different bifurcation phenomena, including global bifurcations as saddle-node on limit cycle and homoclinic bifurcations. The model under investigation can play a role in neuroscience, as it exhibits two different mechanisms of class I neural excitability and one mechanism for class II. It also highlights a mechanism of transition between the two classes.

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Makarenko, V. "Neural Network with Embedded Oscillators." Biological Bulletin 187, no. 2 (1994): 256. http://dx.doi.org/10.1086/bblv187n2p256.

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Wang, Wei, and Jean-Jacques E. Slotine. "Fast computation with neural oscillators." Neurocomputing 69, no. 16-18 (2006): 2320–26. http://dx.doi.org/10.1016/j.neucom.2005.04.012.

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Chung, Hung-Yuan, Chun-Cheng Hou, and Sheng-Yen Hsu. "Hexapod moving in complex terrains via a new adaptive CPG gait design." Industrial Robot: An International Journal 42, no. 2 (2015): 129–41. http://dx.doi.org/10.1108/ir-10-2014-0403.

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Purpose – This paper aims to use the Matsuoka’s neural oscillators as the basic units of central pattern generator (CPG), and to offer a new CPG architecture consisting of a dual neural CPG of circular three links responsible for oscillator phase adjustment, to which an external neural oscillator is added, which is responsible for oscillator amplitude adjustment, to control foot depth to balance itself when treading on an obstacle. Design/methodology/approach – It is equipped with a triaxial accelerometer and a triaxial gyroscope to obtain a real-time robot attitude, and to disintegrate the foot tilt in each direction as feedback signals to CPG to restore the robot’ horizontal attitude on an uneven terrain. The CPG controller is a distributed control method, with each foot controller consisting of a group of reciprocally coupling neural oscillators and sensors to generate different locomotion by different coupling patterns. Findings – The experiment results indicated that the gait design method succeeded in enabling a steady hexapod walking on a rugged terrain, the mode of response is such that adjustments can only be made when the tilt occurs. Practical implications – The overall control mechanism uses individual foot tilts as the feedback signal input to the neural oscillators to change the amplitude and compare against the reference oscillators of fixed amplitude to generate the foot height reference signals that can balance the body, and then convert the control signals, through a trajectory generator, to foot trajectories from which the actual rotation angle of servo motors can be obtained through inverse kinematics to achieve the effect of restoring the balance when traveling. Originality/value – The controller design based on the bionic CPG model has the ability to restore its balance when its body tilts. In addition to the model’s ability to control locomotion, from the response waveforms of this experiment, it can also be noticed that it can control the foot depth to balance itself when treading on an obstacle, and it can adapt to a changing environment. When the obstacle is removed, the robot can quickly regain its balance.

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Velichko, Andrei, Maksim Belyaev, and Petr Boriskov. "A Model of an Oscillatory Neural Network with Multilevel Neurons for Pattern Recognition and Computing." Electronics 8, no. 1 (2019): 75. http://dx.doi.org/10.3390/electronics8010075.

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The current study uses a novel method of multilevel neurons and high order synchronization effects described by a family of special metrics, for pattern recognition in an oscillatory neural network (ONN). The output oscillator (neuron) of the network has multilevel variations in its synchronization value with the reference oscillator, and allows classification of an input pattern into a set of classes. The ONN model is implemented on thermally-coupled vanadium dioxide oscillators. The ONN is trained by the simulated annealing algorithm for selection of the network parameters. The results demonstrate that ONN is capable of classifying 512 visual patterns (as a cell array 3 × 3, distributed by symmetry into 102 classes) into a set of classes with a maximum number of elements up to fourteen. The classification capability of the network depends on the interior noise level and synchronization effectiveness parameter. The model allows for designing multilevel output cascades of neural networks with high net data throughput. The presented method can be applied in ONNs with various coupling mechanisms and oscillator topology.

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Glyzin, Sergey, and Elena Marushkina. "Disordered Oscillations in a Neural Network of Three Oscillators with a Delayed Broadcast Connection." Modeling and Analysis of Information Systems 25, no. 5 (2018): 572–83. http://dx.doi.org/10.18255/1818-1015-2018-5-572-583.

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A model of neural association of three pulsed neurons with a delayed broadcast connection is considered. It is assumed that the parameters of the problem are chosen near the critical point of stability loss by the homogeneous equilibrium state of the system. Because of the broadcast connection the equation corresponding to one of the oscillators can be detached in the system. The two remaining impulse neurons interact with each other and, in addition, there is a periodic external action, determined by the broadcast neuron. Under these conditions, the normal form of this system is constructed for the values of parameters close to the critical ones on a stable invariant integral manifold. This normal form is reduced to a four-dimensional system with two variables responsible for the oscillation amplitudes, and the other two, defined as the difference between the phase variables of these oscillators with the phase variable of the broadcast oscillator. The obtained normal form has an invariant manifold on which the amplitude and phase variables of the oscillators coincide. The dynamics of the problem on this manifold is described. An important result was obtained on the basis of numerical analysis of the normal form. It turned out that periodic and chaotic oscillatory solutions can occur when the coupling between the oscillators is weakened. Moreover, a cascade of bifurcations associated with the same type of phase rearrangements was discovered, where a self-symmetric stable cycle alternately loses symmetry with the appearance of two symmetrical cycles. A cascade of bifurcations of doubling occurs with each of these cycles with the appearance of symmetric chaotic regimes. With further reduction of the coupling parameter, these symmetric chaotic regimes are combined into a self-symmetric one, which is then rebuilt into a self-symmetric cycle of a more complex form compared to the cycle obtained at the previous step. Then the whole process is repeated. Lyapunov exponents were calculated to study chaotic attractors of the system.

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Baldi, Pierre, and Ronny Meir. "Computing with Arrays of Coupled Oscillators: An Application to Preattentive Texture Discrimination." Neural Computation 2, no. 4 (1990): 458–71. http://dx.doi.org/10.1162/neco.1990.2.4.458.

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Recent experimental findings (Gray et al. 1989; Eckhorn et al. 1988) seem to indicate that rapid oscillations and phase-lockings of different populations of cortical neurons play an important role in neural computations. In particular, global stimulus properties could be reflected in the correlated firing of spatially distant cells. Here we describe how simple coupled oscillator networks can be used to model the data and to investigate whether useful tasks can be performed by oscillator architectures. A specific demonstration is given for the problem of preattentive texture discrimination. Texture images are convolved with different sets of Gabor filters feeding into several corresponding arrays of coupled oscillators. After a brief transient, the dynamic evolution in the arrays leads to a separation of the textures by a phase labeling mechanism. The importance of noise and of long range connections is briefly discussed.

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Bartussek, Jan, A. Kadir Mutlu, Martin Zapotocky, and Steven N. Fry. "Limit-cycle-based control of the myogenic wingbeat rhythm in the fruit fly Drosophila." Journal of The Royal Society Interface 10, no. 80 (2013): 20121013. http://dx.doi.org/10.1098/rsif.2012.1013.

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In many animals, rhythmic motor activity is governed by neural limit cycle oscillations under the control of sensory feedback. In the fruit fly Drosophila melanogaster , the wingbeat rhythm is generated myogenically by stretch-activated muscles and hence independently from direct neural input. In this study, we explored if generation and cycle-by-cycle control of Drosophila 's wingbeat are functionally separated, or if the steering muscles instead couple into the myogenic rhythm as a weak forcing of a limit cycle oscillator. We behaviourally tested tethered flying flies for characteristic properties of limit cycle oscillators. To this end, we mechanically stimulated the fly's ‘gyroscopic’ organs, the halteres, and determined the phase relationship between the wing motion and stimulus. The flies synchronized with the stimulus for specific ranges of stimulus amplitude and frequency, revealing the characteristic Arnol'd tongues of a forced limit cycle oscillator. Rapid periodic modulation of the wingbeat frequency prior to locking demonstrates the involvement of the fast steering muscles in the observed control of the wingbeat frequency. We propose that the mechanical forcing of a myogenic limit cycle oscillator permits flies to avoid the comparatively slow control based on a neural central pattern generator.

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HASHIMOTO, Minoru, and Tomofumi KASUGA. "HUMAN-ROBOT HANDSHAKING USING NEURAL OSCILLATORS." KANSEI Engineering International 8, no. 1 (2009): 73–82. http://dx.doi.org/10.5057/er080404-1.

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Ahson, Syed I., and Ahmad M. Mahmoud. "Pattern segmentation using coupled neural oscillators." Nonlinear Analysis: Theory, Methods & Applications 30, no. 3 (1997): 1295–303. http://dx.doi.org/10.1016/s0362-546x(96)00130-7.

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Inoue, M., and S. Fukushima. "A Neural Network of Chaotic Oscillators." Progress of Theoretical Physics 87, no. 3 (1992): 771–74. http://dx.doi.org/10.1143/ptp/87.3.771.

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Tonnelier, A., S. Meignen, H. Bosch, and J. Demongeot. "Synchronization and desynchronization of neural oscillators." Neural Networks 12, no. 9 (1999): 1213–28. http://dx.doi.org/10.1016/s0893-6080(99)00068-4.

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Nishii, Jun. "Learning model for coupled neural oscillators." Network: Computation in Neural Systems 10, no. 3 (1999): 213–26. http://dx.doi.org/10.1088/0954-898x_10_3_301.

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Kurita, Y., K. Nagata, J. Ueda, and T. Ogasawara. "Rotating manipulation using the neural oscillators." Proceedings of JSME annual Conference on Robotics and Mechatronics (Robomec) 2004 (2004): 150. http://dx.doi.org/10.1299/jsmermd.2004.150_2.

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von der Malsburg, Christoph, and Joachim Buhmann. "Sensory segmentation with coupled neural oscillators." Biological Cybernetics 67, no. 3 (1992): 233–42. http://dx.doi.org/10.1007/bf00204396.

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Aoyagi, Toshio, and Katsunori Kitano. "Retrieval Dynamics in Oscillator Neural Networks." Neural Computation 10, no. 6 (1998): 1527–46. http://dx.doi.org/10.1162/089976698300017296.

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We present an analytical approach that allows us to treat the long-time behavior of the recalling process in an oscillator neural network. It is well known that in coupled oscillatory neuronal systems, under suitable conditions, the original dynamics can be reduced to a simpler phase dynamics. In this description, the phases of the oscillators can be regarded as the timings of the neuronal spikes. To attempt an analytical treatment of the recalling dynamics of such a system, we study a simplified model in which we discretize time and assume a synchronous updating rule. The theoretical results show that the retrieval dynamics is described by recursion equations for some macroscopic parameters, such as an overlap with the retrieval pattern. We then treat the noise components in the local field, which arise from the learning of the unretrieved patterns, as gaussian variables. However, we take account of the temporal correlation between these noise components at different times. In particular, we find that this correlation is essential for correctly predicting the behavior of the retrieval process in the case of autoassociative memory. From the derived equations, the maximal storage capacity and the basin of attraction are calculated and graphically displayed. We also consider the more general case that the network retrieves an ordered sequence of phase patterns. In both cases, the basin of attraction remains sufficiently wide to recall the memorized pattern from a noisy one, even near saturation. The validity of these theoretical results is supported by numerical simulations. We believe that this model serves as a convenient starting point for the theoretical study of retrieval dynamics in general oscillatory systems.

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JIANG, CAN, SHANGJIANG GUO, and YIGANG HE. "DYNAMICS IN TIME-DELAY RECURRENTLY COUPLED OSCILLATORS." International Journal of Bifurcation and Chaos 21, no. 03 (2011): 775–88. http://dx.doi.org/10.1142/s0218127411028787.

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A model of time-delay recurrently coupled spatially segregated neural oscillators is proposed. Each of the oscillators describes the dynamics of average activities of excitatory and inhibitory populations of neurons. Bifurcation analysis shows the richness of the dynamical behaviors in a biophysically plausible parameter region. We find oscillatory multi-stability, hysteresis, and stability switches of the rest state provoked by the time delay as well as the strength of the connections between the oscillators. Then we derive the equation describing the flow on the center manifold that enables us to determine the bifurcation direction and stability of bifurcated periodic solutions and equilibria. We also give some numerical simulations to support our main results.

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Wang, Wei-Ping. "Binary-Oscillator Networks: Bridging a Gap between Experimental and Abstract Modeling of Neural Networks." Neural Computation 8, no. 2 (1996): 319–39. http://dx.doi.org/10.1162/neco.1996.8.2.319.

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This paper proposes a simplified oscillator model, called binary-oscillator, and develops a class of neural network models having binary-oscillators as basic units. The binary-oscillator has a binary dynamic variable v = ±1 modeling the “membrane potential” of a neuron, and due to the presence of a “slow current” (as in a classical relaxation-oscillator) it can oscillate between two states. The purpose of the simplification is to enable abstract algorithmic study on the dynamics of oscillator networks. A binary-oscillator network is formally analogous to a system of stochastic binary spins (atomic magnets) in statistical mechanics.

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Shcherbak, Volodymyr, and Iryna Dmytryshyn. "Estimation of oscillation velocities of oscillator network." Proceedings of the Institute of Applied Mathematics and Mechanics NAS of Ukraine 32 (December 28, 2018): 182–89. http://dx.doi.org/10.37069/1683-4720-2018-32-17.

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The study of the collective behavior of multiscale dynamic processes is currently one of the most urgent problems of nonlinear dynamics. Such systems arise on modelling of many cyclical biological or physical processes. It is of fundamental importance for understanding the basic laws of synchronous dynamics of distributed active subsystems with oscillations, such as neural ensembles, biomechanical models of cardiac or locomotor activity, models of turbulent media, etc. Since the nonlinear oscillations that are observed in such systems have a stable limit cycle , which does not depend on the initial conditions, then a system of interconnected nonlinear oscillators is usually used as a model of multiscale processes. The equations of Lienar type are often used as the main dynamic model of each of these oscillators. In a number of practical control problems of such interconnected oscillators it is necessary to determine the oscillation velocities by known data. This problem is considered as observation problem for nonlinear dynamical system. A new method – a synthesis of invariant relations is used to design a nonlinear observer. The method allows us to represent unknowns as a function of known quantities. The scheme of the construction of invariant relations consists in the expansion of the original dynamical system by equations of some controlled subsystem (integrator). Control in the additional system is used for the synthesis of some relations that are invariant for the extended system and have the attraction property for all of its trajectories. Such relations are considered in observation problems as additional equations for unknown state vector of initial oscillators ensemble. To design the observer, first we introduce a observer for unique oscillator of Lienar type and prove its exponential convergence. This observer is then extended on several coupled Lienar type oscillators. The performance of the proposed method is investigated by numerical simulations.

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ITOH, MAKOTO, and LEON O. CHUA. "MEMRISTOR OSCILLATORS." International Journal of Bifurcation and Chaos 18, no. 11 (2008): 3183–206. http://dx.doi.org/10.1142/s0218127408022354.

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The memristor has attracted phenomenal worldwide attention since its debut on 1 May 2008 issue of Nature in view of its many potential applications, e.g. super-dense nonvolatile computer memory and neural synapses. The Hewlett–Packard memristor is a passive nonlinear two-terminal circuit element that maintains a functional relationship between the time integrals of current and voltage, respectively, viz. charge and flux. In this paper, we derive several nonlinear oscillators from Chua's oscillators by replacing Chua's diodes with memristors.

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Wang, Rubin, Zhikang Zhang, Chi K. Tse, Jingyi Qu, and Jianting Cao. "Neural coding in networks of multi-populations of neural oscillators." Mathematics and Computers in Simulation 86 (December 2012): 52–66. http://dx.doi.org/10.1016/j.matcom.2010.10.029.

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Belatreche, Ammar, Liam Maguire, Martin McGinnity, Liam McDaid, and Arfan Ghani. "Computing with Biologically Inspired Neural Oscillators: Application to Colour Image Segmentation." Advances in Artificial Intelligence 2010 (May 12, 2010): 1–21. http://dx.doi.org/10.1155/2010/405073.

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This paper investigates the computing capabilities and potential applications of neural oscillators, a biologically inspired neural model, to grey scale and colour image segmentation, an important task in image understanding and object recognition. A proposed neural system that exploits the synergy between neural oscillators and Kohonen self-organising maps (SOMs) is presented. It consists of a two-dimensional grid of neural oscillators which are locally connected through excitatory connections and globally connected to a common inhibitor. Each neuron is mapped to a pixel of the input image and existing objects, represented by homogenous areas, are temporally segmented through synchronisation of the activity of neural oscillators that are mapped to pixels of the same object. Self-organising maps form the basis of a colour reduction system whose output is fed to a 2D grid of neural oscillators for temporal correlation-based object segmentation. Both chromatic and local spatial features are used. The system is simulated in Matlab and its demonstration on real world colour images shows promising results and the emergence of a new bioinspired approach for colour image segmentation. The paper concludes with a discussion of the performance of the proposed system and its comparison with traditional image segmentation approaches.

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Han, Seung Kee, Christian Kurrer, and Yoshiki Kuramoto. "Diffusive Interaction Leading to Dephasing of Coupled Neural Oscillators." International Journal of Bifurcation and Chaos 07, no. 04 (1997): 869–76. http://dx.doi.org/10.1142/s0218127497000662.

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It is usually believed that strong diffusive coupling in one of the dynamical variables is well-suited for imposing synchronization of oscillators. But it was recently shown that weak diffusive coupling, counter-intuitively, can lead to dephasing of coupled neural oscillators. In this paper, we investigate how diffusively coupled oscillators become dephasing. For this we study a system of coupled neural oscillators on a limit cycle generated through a homoclinic bifurcation. We examine the asymptotic behavior of diffusive coupling as the control parameter approaches the critical value for which the homoclinic bifurcation occurs. In this study, we show that the gradient of phase velocity near the limit cycle is essential in generating dephasing through diffusive interaction.

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DeLiang Wang. "Emergent synchrony in locally coupled neural oscillators." IEEE Transactions on Neural Networks 6, no. 4 (1995): 941–48. http://dx.doi.org/10.1109/72.392256.

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Fairhurst, D., I. Tyukin, H. Nijmeijer, and C. van Leeuwen. "Observers for Canonic Models of Neural Oscillators." Mathematical Modelling of Natural Phenomena 5, no. 2 (2010): 146–84. http://dx.doi.org/10.1051/mmnp/20105206.

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Gerasimova, S. A., G. V. Gelikonov, A. N. Pisarchik, and V. B. Kazantsev. "Synchronization of optically coupled neural-like oscillators." Journal of Communications Technology and Electronics 60, no. 8 (2015): 900–903. http://dx.doi.org/10.1134/s1064226915070062.

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Han, Seung Kee, Christian Kurrer, and Yoshiki Kuramoto. "Dephasing and Bursting in Coupled Neural Oscillators." Physical Review Letters 75, no. 17 (1995): 3190–93. http://dx.doi.org/10.1103/physrevlett.75.3190.

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