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Journal articles on the topic 'Neural networks (Computer science) Lyapunov exponents'

Author: Grafiati

Published: 4 June 2021

Last updated: 14 February 2022

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1

GULER, N., E. UBEYLI, and I. GULER. "Recurrent neural networks employing Lyapunov exponents for EEG signals classification." Expert Systems with Applications 29, no. 3 (October 2005): 506–14. http://dx.doi.org/10.1016/j.eswa.2005.04.011.

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2

Übeyli, Elif Derya. "Probabilistic neural networks employing Lyapunov exponents for analysis of Doppler ultrasound signals." Computers in Biology and Medicine 38, no. 1 (January 2008): 82–89. http://dx.doi.org/10.1016/j.compbiomed.2007.07.004.

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3

UBEYLI, E. "Recurrent neural networks employing Lyapunov exponents for analysis of doppler ultrasound signals." Expert Systems with Applications 34, no. 4 (May 2008): 2538–44. http://dx.doi.org/10.1016/j.eswa.2007.04.002.

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4

Wang, Cheng-Chi, and Yong-Quan Zhu. "Identification and Machine Learning Prediction of Nonlinear Behavior in a Robotic Arm System." Symmetry 13, no. 8 (August 6, 2021): 1445. http://dx.doi.org/10.3390/sym13081445.

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In this study, the subject of investigation was the dynamic double pendulum crank mechanism used in a robotic arm. The arm is driven by a DC motor though the crank system and connected to a fixed side with a mount that includes a single spring and damping. Robotic arms are now widely used in industry, and the requirements for accuracy are stringent. There are many factors that can cause the induction of nonlinear or asymmetric behavior and even excite chaotic motion. In this study, bifurcation diagrams were used to analyze the dynamic response, including stable symmetric orbits and periodic and chaotic motions of the system under different damping and stiffness parameters. Behavior under different parameters was analyzed and verified by phase portraits, the maximum Lyapunov exponent, and Poincaré mapping. Firstly, to distinguish instability in the system, phase portraits and Poincaré maps were used for the identification of individual images, and the maximum Lyapunov exponents were used for prediction. GoogLeNet and ResNet-50 were used for image identification, and the results were compared using a convolutional neural network (CNN). This widens the convolutional layer and expands pooling to reduce network training time and thickening of the image; this deepens the network and strengthens performance. Secondly, the maximum Lyapunov exponent was used as the key index for the indication of chaos. Gaussian process regression (GPR) and the back propagation neural network (BPNN) were used with different amounts of data to quickly predict the maximum Lyapunov exponent under different parameters. The main finding of this study was that chaotic behavior occurs in the robotic arm system and can be more efficiently identified by ResNet-50 than by GoogLeNet; this was especially true for Poincaré map diagnosis. The results of GPR and BPNN model training on the three types of data show that GPR had a smaller error value, and the GPR-21 × 21 model was similar to the BPNN-51 × 51 model in terms of error and determination coefficient, showing that GPR prediction was better than that of BPNN. The results of this study allow the formation of a highly accurate prediction and identification model system for nonlinear and chaotic motion in robotic arms.

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Cui, Li, Chaoyang Chen, Jie Jin, and Fei Yu. "Dynamic Analysis and FPGA Implementation of New Chaotic Neural Network and Optimization of Traveling Salesman Problem." Complexity 2021 (April 20, 2021): 1–10. http://dx.doi.org/10.1155/2021/5521192.

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A neural network is a model of the brain’s cognitive process, with a highly interconnected multiprocessor architecture. The neural network has incredible potential, in the view of these artificial neural networks inherently having good learning capabilities and the ability to learn different input features. Based on this, this paper proposes a new chaotic neuron model and a new chaotic neural network (CNN) model. It includes a linear matrix, a sine function, and a chaotic neural network composed of three chaotic neurons. One of the chaotic neurons is affected by the sine function. The network has rich chaotic dynamics and can produce multiscroll hidden chaotic attractors. This paper studied its dynamic behaviors, including bifurcation behavior, Lyapunov exponent, Poincaré surface of section, and basins of attraction. In the process of analyzing the bifurcation and the basins of attraction, it was found that the network demonstrated hidden bifurcation phenomena, and the relevant properties of the basins of attraction were obtained. Thereafter, a chaotic neural network was implemented by using FPGA, and the experiment proved that the theoretical analysis results and FPGA implementation were consistent with each other. Finally, an energy function was constructed to optimize the calculation based on the CNN in order to provide a new approach to solve the TSP problem.

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Thoai, Vo Phu, Maryam Shahriari Kahkeshi, Van Van Huynh, Adel Ouannas, and Viet-Thanh Pham. "A Nonlinear Five-Term System: Symmetry, Chaos, and Prediction." Symmetry 12, no. 5 (May 25, 2020): 865. http://dx.doi.org/10.3390/sym12050865.

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Chaotic systems have attracted considerable attention and been applied in various applications. Investigating simple systems and counterexamples with chaotic behaviors is still an important topic. The purpose of this work was to study a simple symmetrical system including only five nonlinear terms. We discovered the system’s rich behavior such as chaos through phase portraits, bifurcation diagrams, Lyapunov exponents, and entropy. Interestingly, multi-stability was observed when changing system’s initial conditions. Chaos of such a system was predicted by applying a machine learning approach based on a neural network.

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YANG, XIAO-SONG, and YAN HUANG. "CHAOS AND HYPERCHAOS IN A CLASS OF SIMPLE CELLULAR NEURAL NETWORKS MODELED BY O.D.E." International Journal of Bifurcation and Chaos 16, no. 09 (September 2006): 2729–36. http://dx.doi.org/10.1142/s0218127406016409.

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This paper presents a new class of chaotic and hyperchaotic low dimensional cellular neural networks modeled by ordinary differential equations with some simple connection matrices. The chaoticity of these neural networks is indicated by positive Lyapunov exponents calculated by a computer.

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8

Gallicchio, Claudio, Alessio Micheli, and Luca Silvestri. "Local Lyapunov exponents of deep echo state networks." Neurocomputing 298 (July 2018): 34–45. http://dx.doi.org/10.1016/j.neucom.2017.11.073.

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9

Ding, Long, Li Cui, Fei Yu, and Jie Jin. "Basin of Attraction Analysis of New Memristor-Based Fractional-Order Chaotic System." Complexity 2021 (April 14, 2021): 1–9. http://dx.doi.org/10.1155/2021/5578339.

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Memristor is the fourth basic electronic element discovered in addition to resistor, capacitor, and inductor. It is a nonlinear gadget with memory features which can be used for realizing chaotic, memory, neural network, and other similar circuits and systems. In this paper, a novel memristor-based fractional-order chaotic system is presented, and this chaotic system is taken as an example to analyze its dynamic characteristics. First, we used Adomian algorithm to solve the proposed fractional-order chaotic system and yield a chaotic phase diagram. Then, we examined the Lyapunov exponent spectrum, bifurcation, SE complexity, and basin of attraction of this system. We used the resulting Lyapunov exponent to describe the state of the basin of attraction of this fractional-order chaotic system. As the local minimum point of Lyapunov exponential function is the stable point in phase space, when this stable point in phase space comes into the lowest region of the basin of attraction, the solution of the chaotic system is yielded. In the analysis, we yielded the solution of the system equation with the same method used to solve the local minimum of Lyapunov exponential function. Our system analysis also revealed the multistability of this system.

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10

Kandıran, Engin, and Avadis Hacınlıyan. "Comparison of Feedforward and Recurrent Neural Network in Forecasting Chaotic Dynamical System." AJIT-e Online Academic Journal of Information Technology 10, no. 37 (April 1, 2019): 31–44. http://dx.doi.org/10.5824/1309-1581.2019.2.002.x.

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Artificial neural networks are commonly accepted as a very successful tool for global function approximation. Because of this reason, they are considered as a good approach to forecasting chaotic time series in many studies. For a given time series, the Lyapunov exponent is a good parameter to characterize the series as chaotic or not. In this study, we use three different neural network architectures to test capabilities of the neural network in forecasting time series generated from different dynamical systems. In addition to forecasting time series, using the feedforward neural network with single hidden layer, Lyapunov exponents of the studied systems are forecasted.

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11

HUANG, WEN-ZHI, and YAN HUANG. "CHAOS, BIFURCATION AND ROBUSTNESS OF A CLASS OF HOPFIELD NEURAL NETWORKS." International Journal of Bifurcation and Chaos 21, no. 03 (March 2011): 885–95. http://dx.doi.org/10.1142/s0218127411028866.

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Chaos, bifurcation and robustness of a new class of Hopfield neural networks are investigated. Numerical simulations show that the simple Hopfield neural networks can display chaotic attractors and limit cycles for different parameters. The Lyapunov exponents are calculated, the bifurcation plot and several important phase portraits are presented as well. By virtue of horseshoes theory in dynamical systems, rigorous computer-assisted verifications for chaotic behavior of the system with certain parameters are given, and here also presents a discussion on the robustness of the original system. Besides this, quantitative descriptions of the complexity of these systems are also given, and a robustness analysis of the system is presented too.

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12

Duan, Shouwu, Wanqing Song, Carlo Cattani, Yakufu Yasen, and He Liu. "Fractional Levy Stable and Maximum Lyapunov Exponent for Wind Speed Prediction." Symmetry 12, no. 4 (April 11, 2020): 605. http://dx.doi.org/10.3390/sym12040605.

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In this paper, a wind speed prediction method was proposed based on the maximum Lyapunov exponent (Le) and the fractional Levy stable motion (fLsm) iterative prediction model. First, the calculation of the maximum prediction steps was introduced based on the maximum Le. The maximum prediction steps could provide the prediction steps for subsequent prediction models. Secondly, the fLsm iterative prediction model was established by stochastic differential. Meanwhile, the parameters of the fLsm iterative prediction model were obtained by rescaled range analysis and novel characteristic function methods, thereby obtaining a wind speed prediction model. Finally, in order to reduce the error in the parameter estimation of the prediction model, we adopted the method of weighted wind speed data. The wind speed prediction model in this paper was compared with GA-BP neural network and the results of wind speed prediction proved the effectiveness of the method that is proposed in this paper. In particular, fLsm has long-range dependence (LRD) characteristics and identified LRD by estimating self-similarity index H and characteristic index α. Compared with fractional Brownian motion, fLsm can describe the LRD process more flexibly. However, the two parameters are not independent because the LRD condition relates them by αH > 1.

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13

Neverlien, Åse, Signe Moe, and Jan T. Gravdahl. "Compressor Surge Control Using Lyapunov Neural Networks." Modeling, Identification and Control: A Norwegian Research Bulletin 41, no. 2 (2020): 41–49. http://dx.doi.org/10.4173/mic.2020.2.1.

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14

Sun, Yuming, Xiangpeng Wang, Qiong Wu, and Nariman Sepehri. "On stability analysis via Lyapunov exponents calculated based on radial basis function networks." International Journal of Control 84, no. 8 (August 2011): 1326–41. http://dx.doi.org/10.1080/00207179.2011.593048.

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15

Karabutov, Nikolay. "Structural Methods of Estimation Lyapunov Exponents Linear Dynamic System." International Journal of Intelligent Systems and Applications 7, no. 10 (September 8, 2015): 1–11. http://dx.doi.org/10.5815/ijisa.2015.10.01.

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Karabutov, Nikolay. "About Lyapunov Exponents Identification for Systems with Periodic Coefficients." International Journal of Intelligent Systems and Applications 10, no. 11 (November 8, 2018): 1–10. http://dx.doi.org/10.5815/ijisa.2018.11.01.

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17

Zheng, Cheng-De, and Fan Xie. "Synchronization of delayed memristive neural networks by establishing novel Lyapunov functional." Neurocomputing 369 (December 2019): 80–91. http://dx.doi.org/10.1016/j.neucom.2019.08.060.

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18

Hai, Liu, Song Yong, and Du Qingfu. "Power Forecasting of Combined Heating and Cooling Systems Based on Chaotic Time Series." Journal of Control Science and Engineering 2015 (2015): 1–7. http://dx.doi.org/10.1155/2015/174203.

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Theoretic analysis shows that the output power of the distributed generation system is nonlinear and chaotic. And it is coupled with the microenvironment meteorological data. Chaos is an inherent property of nonlinear dynamic system. A predicator of the output power of the distributed generation system is to establish a nonlinear model of the dynamic system based on real time series in the reconstructed phase space. Firstly, chaos should be detected and quantified for the intensive studies of nonlinear systems. If the largest Lyapunov exponent is positive, the dynamical system must be chaotic. Then, the embedding dimension and the delay time are chosen based on the improved C-C method. The attractor of chaotic power time series can be reconstructed based on the embedding dimension and delay time in the phase space. By now, the neural network can be trained based on the training samples, which are observed from the distributed generation system. The neural network model will approximate the curve of output power adequately. Experimental results show that the maximum power point of the distributed generation system will be predicted based on the meteorological data. The system can be controlled effectively based on the prediction.

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19

Cavalletti, M., G. Ippoliti, and S. Longhi. "Lyapunov-based switching control using neural networks for a remotely operated vehicle." International Journal of Control 80, no. 7 (July 2007): 1077–91. http://dx.doi.org/10.1080/00207170701222939.

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20

Rego, Rosana Cibely Batista, and Fabio Meneghetti Ugulino de Araujo. "Nonlinear Control System with Reinforcement Learning and Neural Networks Based Lyapunov Functions." IEEE Latin America Transactions 19, no. 8 (August 2021): 1253–60. http://dx.doi.org/10.1109/tla.2021.9475855.

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21

Agarwal, Ravi, Snezhana Hristova, and Donal O’Regan. "Global Mittag—Leffler Synchronization for Neural Networks Modeled by Impulsive Caputo Fractional Differential Equations with Distributed Delays." Symmetry 10, no. 10 (October 10, 2018): 473. http://dx.doi.org/10.3390/sym10100473.

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The synchronization problem for impulsive fractional-order neural networks with both time-varying bounded and distributed delays is studied. We study the case when the neural networks and the fractional derivatives of all neurons depend significantly on the moments of impulses and we consider both the cases of state coupling controllers and output coupling controllers. The fractional generalization of the Razumikhin method and Lyapunov functions is applied. Initially, a brief overview of the basic fractional derivatives of Lyapunov functions used in the literature is given. Some sufficient conditions are derived to realize the global Mittag–Leffler synchronization of impulsive fractional-order neural networks. Our results are illustrated with examples.

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22

Yu, Liu. "Research Design Of An Adaptive Controller Based On Desired Trajectory Compensation Of Neural Networks." Cybernetics and Information Technologies 14, no. 5 (December 1, 2014): 5–16. http://dx.doi.org/10.2478/cait-2014-0039.

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Abstract This paper has designed a variable structure controller based on the nominal compensation of neural networks. The neural network input is the desired trajectory, which eliminates the strict assumptions of the control inputs in conventional neural networks. It also ensures the asymptotic stability of the system closed-loop global exponentials to introduce model compensation and continuous variable structure control rate. By means of Lyapunov stability theory, it is analyzed and researched how to guarantee good transient performance of the control system comprehensively and thoroughly. The theoretic analysis and simulation results demonstrate the efficiency of the method proposed.

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23

Korkobi, Talel, Mohamed Djemel, and Mohamed Chtourou. "Stability Analysis of Neural Networks-Based System Identification." Modelling and Simulation in Engineering 2008 (2008): 1–8. http://dx.doi.org/10.1155/2008/343940.

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This paper treats some problems related to nonlinear systems identification. A stability analysis neural network model for identifying nonlinear dynamic systems is presented. A constrained adaptive stable backpropagation updating law is presented and used in the proposed identification approach. The proposed backpropagation training algorithm is modified to obtain an adaptive learning rate guarantying convergence stability. The proposed learning rule is the backpropagation algorithm under the condition that the learning rate belongs to a specified range defining the stability domain. Satisfying such condition, unstable phenomena during the learning process are avoided. A Lyapunov analysis leads to the computation of the expression of a convenient adaptive learning rate verifying the convergence stability criteria. Finally, the elaborated training algorithm is applied in several simulations. The results confirm the effectiveness of the CSBP algorithm.

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24

Ding, Mengying, and Yali Dong. "Robust Finite-time Boundedness of Discrete-time Neural Networks with Time-varying Delays." WSEAS TRANSACTIONS ON INFORMATION SCIENCE AND APPLICATIONS 17 (February 23, 2021): 146–55. http://dx.doi.org/10.37394/23209.2020.17.18.

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This paper is concerned with the problem of robust finite-time boundedness for the discrete-time neural networks with time-varying delays. By constructing an appropriate Lyapunov-Krasovskii functional, we propose the sufficient conditions which ensure the robust finite-time boundedness of the discrete-time neural networks with time-varying delay in terms of linear matrix inequalities. Then the sufficient conditions of robust finite-time stability for the discrete-time neural networks with time-varying delays are given. Finally, a numerical example is presented to illustrate the efficiency of proposed methods.

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25

Zhihong Man, Hong Ren Wu, Sophie Liu, and Xinghuo Yu. "A New Adaptive Backpropagation Algorithm Based on Lyapunov Stability Theory for Neural Networks." IEEE Transactions on Neural Networks 17, no. 6 (November 2006): 1580–91. http://dx.doi.org/10.1109/tnn.2006.880360.

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26

Zhang, Guobao, Ting Wang, Tao Li, and Shumin Fei. "Multiple integral Lyapunov approach to mixed-delay-dependent stability of neutral neural networks." Neurocomputing 275 (January 2018): 1782–92. http://dx.doi.org/10.1016/j.neucom.2017.10.021.

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27

Zheng, Cheng-De. "Stochastic stability of fuzzy Markovian jump neural networks by multiple integral approach." International Journal of Intelligent Computing and Cybernetics 11, no. 1 (March 12, 2018): 81–105. http://dx.doi.org/10.1108/ijicc-11-2016-0046.

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Purpose The purpose of this paper is to develop a methodology for the stochastically asymptotic stability of fuzzy Markovian jumping neural networks with time-varying delay and continuously distributed delay in mean square. Design/methodology/approach The authors perform Briat Lemma, multiple integral approach and linear convex combination technique to investigate a class of fuzzy Markovian jumping neural networks with time-varying delay and continuously distributed delay. New sufficient criterion is established by linear matrix inequalities conditions. Findings It turns out that the obtained methods are easy to be verified and result in less conservative conditions than the existing literature. Two examples show the effectiveness of the proposed results. Originality/value The novelty of the proposed approach lies in establishing a new Wirtinger-based integral inequality and the use of the Lyapunov functional method, Briat Lemma, multiple integral approach and linear convex combination technique for stochastically asymptotic stability of fuzzy Markovian jumping neural networks with time-varying delay and continuously distributed delay in mean square.

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28

Baoyong Zhang, James Lam, and Shengyuan Xu. "Stability Analysis of Distributed Delay Neural Networks Based on Relaxed Lyapunov–Krasovskii Functionals." IEEE Transactions on Neural Networks and Learning Systems 26, no. 7 (July 2015): 1480–92. http://dx.doi.org/10.1109/tnnls.2014.2347290.

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Munoz-Pacheco, Jesus M., Tonatiuh García-Chávez, Victor R. Gonzalez-Diaz, Gisela de La Fuente-Cortes, and Luz del Carmen del Carmen Gómez-Pavón. "Two New Asymmetric Boolean Chaos Oscillators with No Dependence on Incommensurate Time-Delays and Their Circuit Implementation." Symmetry 12, no. 4 (April 1, 2020): 506. http://dx.doi.org/10.3390/sym12040506.

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This manuscript introduces two new chaotic oscillators based on autonomous Boolean networks (ABN), preserving asymmetrical logic functions. That means that the ABNs require a combination of XOR-XNOR logic functions. We demonstrate analytically that the two ABNs do not have fixed points, and therefore, can evolve to Boolean chaos. Using the Lyapunov exponent’s method, we also prove the chaotic behavior, generated by the proposed chaotic oscillators, is insensitive to incommensurate time-delays paths. As a result, they can be implemented using distinct electronic circuits. More specifically, logic-gates–, GAL–, and FPGA–based implementations verify the theoretical findings. An integrated circuit using a CMOS 180nm fabrication technology is also presented to get a compact chaos oscillator with relatively high-frequency. Dynamical behaviors of those implementations are analyzed using time-series, time-lag embedded attractors, frequency spectra, Poincaré maps, and Lyapunov exponents.

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30

Duan, Wenyong, Yan Li, and Jian Chen. "Further Stability Analysis for Time-Delayed Neural Networks Based on an Augmented Lyapunov Functional." IEEE Access 7 (2019): 104655–66. http://dx.doi.org/10.1109/access.2019.2931714.

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31

Chang, Xin, Qinkun Xiao, Yilin Zhu, and Jielei Xiao. "Stability Analysis of Two Kinds of Fractional-Order Neural Networks Based on Lyapunov Method." IEEE Access 9 (2021): 124132–41. http://dx.doi.org/10.1109/access.2021.3110764.

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32

Kim, Myung-Hyun, and Daniel J. Inman. "Direct Adaptive Control of Underwater Vehicles using Neural Networks." Journal of Vibration and Control 9, no. 5 (May 2003): 605–19. http://dx.doi.org/10.1177/1077546303009005006.

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A direct adaptive neural network controller is developed for a model of an underwater vehicle. A radial basis neural network and a multilayer neural network are used in the closed-loop to approximate the nonlinear vehicle dynamics. No prior off-line training phase and no explicit knowledge of the structure of the plant are required, and this scheme exploits the advantages of both neural network control and adaptive control. A control law and a stable on-line adaptive law are derived using the Lyapunov theory, and the convergence of the tracking error to zero and the boundedness of signals are guaranteed. A comparison of the results with different neural network architecture is made, and the performance of the controller is demonstrated by computer simulations.

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Xueli, Wu, Zhang Jianhua, Guan Xinping, and Meng Hua. "Delay‐dependent asymptotic stability of BAM neural networks with time delay." Kybernetes 39, no. 8 (August 10, 2010): 1313–21. http://dx.doi.org/10.1108/03684921011063600.

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PurposeThe purpose of this paper is to examine the criteria of uniqueness of the equilibrium point and the new stability criteria for stability of the equilibrium point. The new stability condition is dependent on the size of delays.Design/methodology/approachThe global asymptotic stability of a class of delayed bi‐directional associative memory (BAM) neural networks is studied. Some new sufficient conditions are presented for the unique equilibrium point and the global stability of BAM neural networks with time delays by constructing Lyapunov functions and using the linear matrix inequality. A numerical example is presented to illustrate the effectiveness of the theoretical results.FindingsBased on the mathematical method and matrixes inequality skill, some criteria are obtained which contain the unique equilibrium point and the global stability of BAM neural networks.Research limitations/implicationsThe paper proposes the new Lyapunov function and new skill to compose matrixes inequality.Practical implicationsA very useful method for BAM neural network to judge the uniqueness of the equilibrium point and stability.Originality/valueThe new mathematical model is proposed about the production process, and the new control method is used in the temperature system for a double layers welded pipe in welding process.

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Wang, Shuang, Hai Zhang, Weiwei Zhang, and Hongmei Zhang. "Finite-Time Projective Synchronization of Caputo Type Fractional Complex-Valued Delayed Neural Networks." Mathematics 9, no. 12 (June 17, 2021): 1406. http://dx.doi.org/10.3390/math9121406.

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This paper focuses on investigating the finite-time projective synchronization of Caputo type fractional-order complex-valued neural networks with time delay (FOCVNNTD). Based on the properties of fractional calculus and various inequality techniques, by constructing suitable the Lyapunov function and designing two new types controllers, i.e., feedback controller and adaptive controller, two sufficient criteria are derived to ensure the projective finite-time synchronization between drive and response systems, and the synchronization time can effectively be estimated. Finally, two numerical examples are presented to verify the effectiveness and feasibility of the proposed results.

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Xu, Changjin, and Peiluan Li. "The anti-periodic oscillations of shunting inhibitory cellular neural networks with time-varying delays and continuously distributed delays." International Journal of Intelligent Computing and Cybernetics 10, no. 4 (November 13, 2017): 513–29. http://dx.doi.org/10.1108/ijicc-11-2016-0053.

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Purpose The purpose of this paper is to study the existence and exponential stability of anti-periodic solutions of a class of shunting inhibitory cellular neural networks (SICNNs) with time-varying delays and continuously distributed delays. Design/methodology/approach The inequality technique and Lyapunov functional method are applied. Findings Sufficient conditions are obtained to ensure that all solutions of the networks converge exponentially to the anti-periodic solution, which are new and complement previously known results. Originality/value There are few papers that deal with the anti-periodic solutions of delayed SICNNs with the form negative feedback – aij(t)αij(xij(t)).

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Liu, Weide, Jianliang Huang, and Qinghe Yao. "Stability Analysis of Pseudo-Almost Periodic Solution for a Class of Cellular Neural Network with D Operator and Time-Varying Delays." Mathematics 9, no. 16 (August 15, 2021): 1951. http://dx.doi.org/10.3390/math9161951.

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Cellular neural networks with D operator and time-varying delays are found to be effective in demonstrating complex dynamic behaviors. The stability analysis of the pseudo-almost periodic solution for a novel neural network of this kind is considered in this work. A generalized class neural networks model, combining cellular neural networks and the shunting inhibitory neural networks with D operator and time-varying delays is constructed. Based on the fixed-point theory and the exponential dichotomy of linear equations, the existence and uniqueness of pseudo-almost periodic solutions are investigated. Through a suitable variable transformation, the globally exponentially stable sufficient condition of the cellular neural network is examined. Compared with previous studies on the stability of periodic solutions, the global exponential stability analysis for this work avoids constructing the complex Lyapunov functional. Therefore, the stability criteria of the pseudo-almost periodic solution for cellular neural networks in this paper are more precise and less conservative. Finally, an example is presented to illustrate the feasibility and effectiveness of our obtained theoretical results.

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37

Raja, Ramachandran, Rathinasamy Sakthivel, Selvaraj Anthoni, and Hyunsoo Kim. "Stability of impulsive Hopfield neural networks with Markovian switching and time-varying delays." International Journal of Applied Mathematics and Computer Science 21, no. 1 (March 1, 2011): 127–35. http://dx.doi.org/10.2478/v10006-011-0009-y.

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Stability of impulsive Hopfield neural networks with Markovian switching and time-varying delaysThe paper is concerned with stability analysis for a class of impulsive Hopfield neural networks with Markovian jumping parameters and time-varying delays. The jumping parameters considered here are generated from a continuous-time discrete-state homogenous Markov process. By employing a Lyapunov functional approach, new delay-dependent stochastic stability criteria are obtained in terms of linear matrix inequalities (LMIs). The proposed criteria can be easily checked by using some standard numerical packages such as the Matlab LMI Toolbox. A numerical example is provided to show that the proposed results significantly improve the allowable upper bounds of delays over some results existing in the literature.

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38

Chen, Yun, and Gang Chen. "Stability analysis of delayed neural networks based on a relaxed delay-product-type Lyapunov functional." Neurocomputing 439 (June 2021): 340–47. http://dx.doi.org/10.1016/j.neucom.2021.01.098.

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39

Xia, Yannan, Xiaofeng Chen, Dongyuan Lin, and Zhongshan Li. "Some Dynamical Behaviors of Fractional-Order Commutative Quaternion-Valued Neural Networks via Direct Method of Lyapunov." IEEE Access 9 (2021): 693–708. http://dx.doi.org/10.1109/access.2020.3046842.

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40

Hai, Quan. "Sampled-Data Synchronization Control for Chaotic Neural Networks With Mixed Delays: A Discontinuous Lyapunov Functional Approach." IEEE Access 9 (2021): 25383–93. http://dx.doi.org/10.1109/access.2021.3057918.

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41

Rajchakit, Grienggrai, Ramalingam Sriraman, Chee Peng Lim, Panu Sam-ang, and Porpattama Hammachukiattikul. "Synchronization in Finite-Time Analysis of Clifford-Valued Neural Networks with Finite-Time Distributed Delays." Mathematics 9, no. 11 (May 21, 2021): 1163. http://dx.doi.org/10.3390/math9111163.

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In this paper, we explore the finite-time synchronization of Clifford-valued neural networks with finite-time distributed delays. To address the problem associated with non-commutativity pertaining to the multiplication of Clifford numbers, the original n-dimensional Clifford-valued drive and response systems are firstly decomposed into the corresponding 2m-dimensional real-valued counterparts. On the basis of a new Lyapunov–Krasovskii functional, suitable controller and new computational techniques, finite-time synchronization criteria are formulated for the corresponding real-valued drive and response systems. The feasibility of the main results is verified by a numerical example.

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Li, Guangshi. "Adaptive Sliding Mode Control for a Class of Manipulator Systems with Output Constraint." Complexity 2021 (February 3, 2021): 1–7. http://dx.doi.org/10.1155/2021/6642795.

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In this paper, an adaptive sliding mode control method based on neural networks is presented for a class of manipulator systems. The main characteristic of the discussed system is that the output variable is required to keep within a constraint set. In order to ensure that the system output meets the time-varying constraint condition, the asymmetric barrier Lyapunov function is selected in the design process. According to Lyapunov stability theory, the stability of the closed-loop system is analyzed. It is demonstrated that all signals in the resulted system are bounded, the tracking error converges to a small compact set, and the system output limits in its constrained set. Finally, the simulation example is used to show the effectiveness of the presented control strategy.

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Liu, Yang, Rongjiang Yang, Jianquan Lu, Bo Wu, and Xiushan Cai. "Stability analysis of high-order Hopfield-type neural networks based on a new impulsive differential inequality." International Journal of Applied Mathematics and Computer Science 23, no. 1 (March 1, 2013): 201–11. http://dx.doi.org/10.2478/amcs-2013-0016.

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This paper is devoted to studying the globally exponential stability of impulsive high-order Hopfield-type neural networks with time-varying delays. In the process of impulsive effect, nonlinear and delayed factors are simultaneously considered. A new impulsive differential inequality is derived based on the Lyapunov-Razumikhin method and some novel stability criteria are then given. These conditions, ensuring the global exponential stability, are simpler and less conservative than some of the previous results. Finally, two numerical examples are given to illustrate the advantages of the obtained results.

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Xu, Yao, Renren Wang, Hongqian Lu, Xingxing Song, Yahan Deng, and Wuneng Zhou. "Adaptive Event-Triggered Synchronization of Networked Neural Networks with Time-Varying Delay Subject to Actuator Saturation." Complexity 2021 (July 7, 2021): 1–14. http://dx.doi.org/10.1155/2021/9957624.

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This paper discusses the adaptive event-triggered synchronization problem of a class of neural networks (NNs) with time-varying delay and actuator saturation. First, in view of the limited communication channel capacity of the network system and unnecessary data transmission in the NCSs, an adaptive event-triggered scheme (AETS) is introduced to reduce the network load and improve network utilization. Second, under the AETS, the synchronization error model of the delayed master-slave synchronization system is constructed with actuator saturation. Third, based on Lyapunov–Krasovskii functional (LKF), a new sufficient criterion to guarantee the asymptotic stability of the synchronization error system is derived. Moreover, by solving the stability criterion expressed in the form of a set of linear matrix inequalities (LMIs), some necessary parameters of the system are obtained. At last, two examples are expressed to demonstrate the feasibility of this method.

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Hua, Changchun, Yibo Wang, and Shuangshuang Wu. "Stability analysis of neural networks with time-varying delay using a new augmented Lyapunov–Krasovskii functional." Neurocomputing 332 (March 2019): 1–9. http://dx.doi.org/10.1016/j.neucom.2018.08.044.

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Zhang, Xian-Ming, Qing-Long Han, Xiaohua Ge, and Bao-Lin Zhang. "Passivity Analysis of Delayed Neural Networks Based on Lyapunov–Krasovskii Functionals With Delay-Dependent Matrices." IEEE Transactions on Cybernetics 50, no. 3 (March 2020): 946–56. http://dx.doi.org/10.1109/tcyb.2018.2874273.

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Zheng, Cheng-De, and Zhanshan Wang. "Stochastic synchronization of neutral-type chaotic impulse neural networks with leakage delay and Markovian jumping parameters." International Journal of Intelligent Computing and Cybernetics 9, no. 3 (August 8, 2016): 237–54. http://dx.doi.org/10.1108/ijicc-12-2015-0043.

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Purpose The purpose of this paper is to develop a methodology for the stochastically asymptotic synchronization problem for a class of neutral-type chaotic neural networks with both leakage delay and Markovian jumping parameters under impulsive perturbations. Design/methodology/approach The authors perform drive-response concept and time-delay feedback control techniques to investigate a class of neutral-type chaotic neural networks with both leakage delay and Markovian jumping parameters under impulsive perturbations. New sufficient criterion is established without strict conditions imposed on the activation functions. Findings It turns out that the approach results in new sufficient criterion easy to be verified but without the usual assumption of the differentiability and monotonicity of the activation functions. Two examples show the effectiveness of the obtained results. Originality/value The novelty of the proposed approach lies in removing the usual assumption of the differentiability and monotonicity of the activation functions, and the use of the Lyapunov functional method, Jensen integral inequality, a novel Gu’s lemma, reciprocal convex and linear convex combination technique for the stochastically asymptotic synchronization problem for a class of neutral-type chaotic neural networks with both leakage delay and Markovian jumping parameters under impulsive perturbations.

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LOU, XU-YANG, and BAO-TONG CUI. "DELAY-DEPENDENT GLOBAL ROBUST ASYMPTOTIC STABILITY ANALYSIS OF BAM NEURAL NETWORKS WITH TIME DELAY: AN LMI APPROACH." New Mathematics and Natural Computation 03, no. 01 (March 2007): 57–68. http://dx.doi.org/10.1142/s1793005707000628.

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The global robust asymptotic stability of bi-directional associative memory (BAM) neural networks with constant or time-varying delays is studied. An approach combining the Lyapunov-Krasovskii functional with the linear matrix inequality (LMI) is taken to study the problem. Some a criteria for the global robust asymptotic stability, which gives information on the delay-dependent property, are derived. Some illustrative examples are given to demonstrate the effectiveness of the obtained results.

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Fuentes-Aguilar, Rita Q., and Isaac Chairez. "Adaptive Tracking Control of State Constraint Systems Based on Differential Neural Networks: A Barrier Lyapunov Function Approach." IEEE Transactions on Neural Networks and Learning Systems 31, no. 12 (December 2020): 5390–401. http://dx.doi.org/10.1109/tnnls.2020.2966914.

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Park, J. W., R. G. Harley, and G. K. Venayagamoorthy. "Indirect Adaptive Control for Synchronous Generator: Comparison of MLP/RBF Neural Networks Approach With Lyapunov Stability Analysis." IEEE Transactions on Neural Networks 15, no. 2 (March 2004): 460–64. http://dx.doi.org/10.1109/tnn.2004.824260.

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