Journal articles: 'Hodgkin-Huxley model'

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He, Ji-Huan. "A modified Hodgkin–Huxley model." Chaos, Solitons & Fractals 29, no. 2 (July 2006): 303–6. http://dx.doi.org/10.1016/j.chaos.2005.08.144.

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Guckenheimer, John, and Ricardo A. Oliva. "Chaos in the Hodgkin--Huxley Model." SIAM Journal on Applied Dynamical Systems 1, no. 1 (January 2002): 105–14. http://dx.doi.org/10.1137/s1111111101394040.

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McCormick, David A., Yousheng Shu, and Yuguo Yu. "Hodgkin and Huxley model — still standing?" Nature 445, no. 7123 (January 2007): E1—E2. http://dx.doi.org/10.1038/nature05523.

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Cano, Gaspar, and Rui Dilão. "Intermittency in the Hodgkin-Huxley model." Journal of Computational Neuroscience 43, no. 2 (June 14, 2017): 115–25. http://dx.doi.org/10.1007/s10827-017-0653-9.

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Wang, Lin, Ying Jie Wang, Xiao Yu Chen, and Xiao Qiang Liang. "Soliton Solutions and Applications on Neuronal Hodgkin-Huxley Model." Applied Mechanics and Materials 411-414 (September 2013): 3265–68. http://dx.doi.org/10.4028/www.scientific.net/amm.411-414.3265.

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from one neuron to another neuron fibers generate action potentials of nerve cells, leading to nervous excitement along. Hodgkin - Huxley neuron model has been used to solve many physiological phenomenon. This paper presents Neuralfiber conduction theory, based on the Hodgkin - Huxley model, considering the propagation of nerve impulses nerve fiber soliton solutions, and to further discuss the application of numerical results are two aspects raised.

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Bazsó, Fülöp, László Zalányi, and Gábor Csárdi. "Channel noise in Hodgkin–Huxley model neurons." Physics Letters A 311, no. 1 (May 2003): 13–20. http://dx.doi.org/10.1016/s0375-9601(03)00454-7.

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Coutin, Laure, Jean-Marc Guglielmi, and Nicolas Marie. "On a fractional stochastic Hodgkin–Huxley model." International Journal of Biomathematics 11, no. 05 (July 2018): 1850061. http://dx.doi.org/10.1142/s1793524518500614.

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The model studied in this paper is a stochastic extension of the so-called neuron model introduced by Hodgkin and Huxley. In the sense of rough paths, the model is perturbed by a multiplicative noise driven by a fractional Brownian motion, with a vector field satisfying the viability condition of Coutin and Marie for [Formula: see text]. An application to the modeling of the membrane potential of nerve fibers damaged by a neuropathy is provided.

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Shama, Farzin, Saeed Haghiri, and Mohammad Amin Imani. "FPGA Realization of Hodgkin-Huxley Neuronal Model." IEEE Transactions on Neural Systems and Rehabilitation Engineering 28, no. 5 (May 2020): 1059–68. http://dx.doi.org/10.1109/tnsre.2020.2980475.

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Naundorf, Björn, Fred Wolf, and Maxim Volgushev. "Hodgkin and Huxley model — still standing? (Reply)." Nature 445, no. 7123 (January 2007): E2—E3. http://dx.doi.org/10.1038/nature05534.

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Shorten, P. "A Hodgkin–Huxley Model Exhibiting Bursting Oscillations." Bulletin of Mathematical Biology 62, no. 4 (July 2000): 695–715. http://dx.doi.org/10.1006/bulm.2000.0172.

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Tejo, Mauricio. "Stochastic Nonlinear Equations Describing the Mesoscopic Voltage-Gated Ion Channels." International Journal of Stochastic Analysis 2015 (April 5, 2015): 1–13. http://dx.doi.org/10.1155/2015/658342.

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We propose a stochastic nonlinear system to model the gating activity coupled with the membrane potential for a typical neuron. It distinguishes two different levels: a macroscopic one, for the membrane potential, and a mesoscopic one, for the gating process through the movement of its voltage sensors. Such a nonlinear system can be handled to form a Hodgkin-Huxley-like model, which links those two levels unlike the original deterministic Hodgkin-Huxley model which is positioned at a macroscopic scale only. Also, we show that an interacting particle system can be used to approximate our model, which is an approximation technique similar to the jump Markov processes, used to approximate the original Hodgkin-Huxley model.

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Islam, Molla Manjurul, and Naimul Islam. "Measuring Threshold Potentials of Neuron Cells Using Hodgkin-Huxley Model by Applying Different Types of Input Signals." Dhaka University Journal of Science 64, no. 1 (June 28, 2016): 15–20. http://dx.doi.org/10.3329/dujs.v64i1.28518.

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The Hodgkin-Huxley model is the first successful mathematical model for explaining the initiation and propagation of an action potential in a neuron cell. In this paper we reinvestigated the Hodgkin-Huxley model through computer simulation and determined the threshold potentials by applying different types of stimulating input signals. To implement the work, a computer programme of the Hodgkin-Huxley model was written in MATLAB programming language. The action potentials of neuron cells were checked and the threshold potentials of the neuron cell for specific types of stimulating input signals were tabulated with an aim to utilize these values to do experiment on neuron cell in future.Dhaka Univ. J. Sci. 64(1): 15-20, 2016 (January)

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Johnson, Melissa G., and Sylvain Chartier. "Spike neural models (part I): The Hodgkin-Huxley model." Quantitative Methods for Psychology 13, no. 2 (May 1, 2017): 105–19. http://dx.doi.org/10.20982/tqmp.13.2.p105.

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Foster, W. R., L. H. Ungar, and J. S. Schwaber. "Significance of conductances in Hodgkin-Huxley models." Journal of Neurophysiology 70, no. 6 (December 1, 1993): 2502–18. http://dx.doi.org/10.1152/jn.1993.70.6.2502.

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1. We explore the roles of conductances in Hodgkin-Huxley (HH) models using a method that allows the explicit linking of HH model input-output behavior to parameter values for maximal conductances, voltage shifts, and time constants. The procedure can be used to identify not only the parameter values most critical to supporting a neuronal activity pattern of interest but also the relationships between parameters which may be required, e.g., limited ranges of relative magnitudes. 2. The method is the repeated use of stochastic search to find hundreds or even thousands of different sets of model parameter values that allow a HH model to produce a desired behavior, such as current-frequency transduction, to within a desired tolerance, e.g., frequency match to within 10 Hz. Graphical or other analysis may then be performed to reveal the shape and boundaries of the parameter solution regions that support the desired behavior. 3. The shape of these parameter regions can reveal parameter values and relationships essential to the behavior. For instance, graphical display may reveal covariances between maximal conductance values, or a much wider range of variation in some maximal conductance values than in others. 4. We demonstrate the use of these techniques with simple, representative HH models, primarily that of Connor et al. for crustacean walking leg axons, but also some extensions of the results are explored using the more complex model of McCormick and Huguenard for thalamocortical relay neurons. Both models are single compartment. Behaviors studied include current-to-frequency transduction, the time delay to first action potential in response to current steps, and the timing of action potential occurrences in response to both square-wave current injection and the injection of currents derived from in vitro records of excitatory postsynaptic currents. 5. Using these simple models, we find that relatively general behaviors such as current-frequency (I/F) curves may be supported by very broad, but bounded parameter solution regions, with the shape of the solution regions revealing the relative importance of the maximal conductances of a model in creating the behavior. Furthermore, we find that a focus on increasingly specific behaviors, such as I/F behavior, defined by tolerances of only a few hertz combined with strict requirements for action potential height, inevitably leads to increasingly narrow, and eventually nonphysiologically narrow, regions of acceptable parameter values. 6. We use the Connor et al. model to reproduce the in vitro action potential timing responses of a rat brain stem neuron to various stimuli.(ABSTRACT TRUNCATED AT 400 WORDS)

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YOSHINAGA, TETSUYA, YASUHIKO SANO, and HIROSHI KAWAKAMI. "A METHOD TO CALCULATE BIFURCATIONS IN SYNAPTICALLY COUPLED HODGKIN–HUXLEY EQUATIONS." International Journal of Bifurcation and Chaos 09, no. 07 (July 1999): 1451–58. http://dx.doi.org/10.1142/s0218127499001000.

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We propose a numerical method for calculating bifurcations of periodic solutions observed in a model equation of Hodgkin–Huxley neurons coupled by excitatory synapses with a time delay. To illustrate the validity of the method, bifurcations in two-coupled Hodgkin–Huxley equations with variation of a coupling coefficient and time delay are studied.

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Rodríguez-Collado, Alejandro, and Cristina Rueda. "A simple parametric representation of the Hodgkin-Huxley model." PLOS ONE 16, no. 7 (July 22, 2021): e0254152. http://dx.doi.org/10.1371/journal.pone.0254152.

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The Hodgkin-Huxley model, decades after its first presentation, is still a reference model in neuroscience as it has successfully reproduced the electrophysiological activity of many organisms. The primary signal in the model represents the membrane potential of a neuron. A simple representation of this signal is presented in this paper. The new proposal is an adapted Frequency Modulated Möbius multicomponent model defined as a signal plus error model in which the signal is decomposed as a sum of waves. The main strengths of the method are the simple parametric formulation, the interpretability and flexibility of the parameters that describe and discriminate the waveforms, the estimators’ identifiability and accuracy, and the robustness against noise. The approach is validated with a broad simulation experiment of Hodgkin-Huxley signals and real data from squid giant axons. Interesting differences between simulated and real data emerge from the comparison of the parameter configurations. Furthermore, the potential of the FMM parameters to predict Hodgkin-Huxley model parameters is shown using different Machine Learning methods. Finally, promising contributions of the approach in Spike Sorting and cell-type classification are detailed.

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Díaz M., Jose A., Oscar Téquita, and Fernando Naranjo. "Neuronal Synchronization of Electrical Activity, Using the Hodgkin-Huxley Model and RCLSJ Circuit." Ingeniería y Ciencia 12, no. 23 (February 2016): 93–106. http://dx.doi.org/10.17230/ingciencia.12.23.5.

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We simulated the neuronal electrical activity using the Hodgkin-Huxleymodel (HH) and a superconductor circuit, containing Josephson junctions. These HH model make possible simulate the main neuronal dynamics characteristics such as action potentials, firing thres hold and refractory period.The purpose of the manuscript is show a method to syncronize a RCL-shunted Josephson junction to a neuronal dynamics represented by the HH model. Thus the RCLSJ circuit is able to mimics the behavior of the HH neuron. We controlated the RCLSJ circuit, using and improved adaptative track scheme, that with the improved Lyapunov functions and thetwo controllable gain coefficients allowing synchronization of two neuronal models. Results will provide the path to follow forward the understanding neuronal networks synchronization about, generating the intrinsic brain behavior.

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Marceniuk, V. P., and Z. V. Mayhruk. "Algorithms qualitative analysis Hodgkin–Huxley model axon activity." Klinical Informatics and Telemedicine 11, no. 121 (January 30, 2015): 43–49. http://dx.doi.org/10.31071/kit2015.12.06.

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Chen, Xiao Yu, Lin Wang, Ying Jie Wang, and Xiao Qiang Liang. "Study on Hodgkin-Huxley Neuron Model under Disturbance." Applied Mechanics and Materials 411-414 (September 2013): 3261–64. http://dx.doi.org/10.4028/www.scientific.net/amm.411-414.3261.

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Nerve cells can respond to external electromagnetic environment. It features mainly depends on the characteristics of the interference conditions. Hodgkin - Huxley (HH) model gives a quantitative description of neuronal action potentials, many electrophysiological properties of nerve cells and biological rhythms issues of interpretation, the nervous system in order to study the effect of noise, this paper considers the environment in result of the presence of the electric field coupling, and the electric field in the body of the response characteristics of HH model, given values of the simulation results and analysis of the effect of disturbance characteristics of neurons as a disturbance conditions neuronal activity.

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Rutherford, George H., Zach D. Mobille, Jordan Brandt-Trainer, Rosangela Follmann, and Epaminondas Rosa. "Analog implementation of a Hodgkin–Huxley model neuron." American Journal of Physics 88, no. 11 (November 2020): 918–23. http://dx.doi.org/10.1119/10.0001072.

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Colwell, Lucy J., and Michael P. Brenner. "Action Potential Initiation in the Hodgkin-Huxley Model." PLoS Computational Biology 5, no. 1 (January 16, 2009): e1000265. http://dx.doi.org/10.1371/journal.pcbi.1000265.

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Takahata, Takayuki, Seiji Tanabe, and K. Pakdaman. "White-noise stimulation of the Hodgkin-Huxley model." Biological Cybernetics 86, no. 5 (May 1, 2002): 403–17. http://dx.doi.org/10.1007/s00422-002-0308-3.

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Jin, Wu-yin, Jian-xue Xu, Ying Wu, Ling Hong, and Yao-bing Wei. "Crisis of interspike intervals in Hodgkin–Huxley model." Chaos, Solitons & Fractals 27, no. 4 (February 2006): 952–58. http://dx.doi.org/10.1016/j.chaos.2005.04.062.

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Valle, Jemy A. Mandujano, and Alexandre L. Madureira. "Parameter Identification Problem in the Hodgkin-Huxley Model." Neural Computation 34, no. 4 (March 23, 2022): 939–70. http://dx.doi.org/10.1162/neco_a_01487.

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Abstract The Hodgkin-Huxley (H-H) landmark model is described by a system of four nonlinear differential equations that describes how action potentials in neurons are initiated and propagated. However, obtaining some of the parameters of the model requires a tedious combination of experiments and data tuning. In this letter, we propose the use of a minimal error iteration method to estimate some of the parameters in the H-H model, given the measurements of membrane potential. We provide numerical results showing that the approach approximates well some of the model's parameters, using the measured voltage as data, even in the presence of noise.

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PHILLIPSON, PAUL E., and PETER SCHUSTER. "A COMPARATIVE STUDY OF THE HODGKIN–HUXLEY AND FITZHUGH–NAGUMO MODELS OF NEURON PULSE PROPAGATION." International Journal of Bifurcation and Chaos 15, no. 12 (December 2005): 3851–66. http://dx.doi.org/10.1142/s0218127405014349.

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The four-dimensional Hodgkin–Huxley equations are considered as the prototype for description of neural pulse propagation. Their mathematical complexity and sophistication prompted a simplified two-dimensional model, the FitzHugh–Nagumo equations, which display many of the former's dynamical features. Numerical and mathematical analysis are employed to demonstrate that the FitzHugh–Nagumo equations can provide quantitative predictions in close agreement with the Hodgkin–Huxley equations. The two most important parameters of a neural pulse are its speed c(T) and pulse height v max (T) and so numerical computations of these quantities predicted by the Hodgkin–Huxley equations are given over the entire temperature range T for stability of a neural pulse. Similarly, the FitzHugh–Nagumo equations are parameterized by two dimensionless quantities: a which determines the dynamics of the pulse front, and b whose departure from zero tailors the front to form the resultant pulse. Parallel computations are presented for the FitzHugh–Nagumo pulse whose relative simplicity permits analytic determination to close approximation of the dimensionless speed θ(a, b) and pulse height V max (a, b). It is shown that the two models are numerically identified by scaling according to c = 4904 θ cm/sec and v max = 115 V max mV where the numbers are a consequence of the experimental parameter values inherent to the Hodgkin–Huxley equations. With this connection, at a given temperature the Hodgkin–Huxley speed and pulse height determine unique values for the two FitzHugh–Nagumo parameters a and b. Approximate analytic solution for θ(a, b) allows construction of a three-dimensional [a, b, θ] state plot upon which a unique ridge defines, as a function of temperature, the speed and associated pulse height predicted by the Hodgkin–Huxley equations. The generality of the state plot suggests its application to other conductance models. Comparison of the Hodgkin–Huxley with the FitzHugh–Nagumo models highlight the quantitative limitations of the latter in the region of the minimum characterizing the back portion of the pulse. To overcome this limitation would require analytic extension of the FitzHugh–Nagumo dynamics to higher dimensionality.

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Gonzalez-Raya, Tasio, Enrique Solano, and Mikel Sanz. "Quantized Three-Ion-Channel Neuron Model for Neural Action Potentials." Quantum 4 (January 20, 2020): 224. http://dx.doi.org/10.22331/q-2020-01-20-224.

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The Hodgkin-Huxley model describes the conduction of the nervous impulse through the axon, whose membrane's electric response can be described employing multiple connected electric circuits containing capacitors, voltage sources, and conductances. These conductances depend on previous depolarizing membrane voltages, which can be identified with a memory resistive element called memristor. Inspired by the recent quantization of the memristor, a simplified Hodgkin-Huxley model including a single ion channel has been studied in the quantum regime. Here, we study the quantization of the complete Hodgkin-Huxley model, accounting for all three ion channels, and introduce a quantum source, together with an output waveguide as the connection to a subsequent neuron. Our system consists of two memristors and one resistor, describing potassium, sodium, and chloride ion channel conductances, respectively, and a capacitor to account for the axon's membrane capacitance. We study the behavior of both ion channel conductivities and the circuit voltage, and we compare the results with those of the single channel, for a given quantum state of the source. It is remarkable that, in opposition to the single-channel model, we are able to reproduce the voltage spike in an adiabatic regime. Arguing that the circuit voltage is a quantum variable, we find a purely quantum-mechanical contribution in the system voltage's second moment. This work represents a complete study of the Hodgkin-Huxley model in the quantum regime, establishing a recipe for constructing quantum neuron networks with quantum state inputs. This paves the way for advances in hardware-based neuromorphic quantum computing, as well as quantum machine learning, which might be more efficient resource-wise.

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Bashkirtseva, Irina, and Lev Ryashko. "Stochastic Sensitivity and Method of Principal Directions in Excitability Analysis of the Hodgkin–Huxley Model." International Journal of Bifurcation and Chaos 29, no. 13 (December 10, 2019): 1950186. http://dx.doi.org/10.1142/s0218127419501864.

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We study the probabilistic behavior of the Hodgkin–Huxley neuron model in the presence of random forcing of the external current parameter. The stochastic excitement in the zone of stable equilibria is illustrated by the statistics of interspike intervals and probabilistic distributions of mixed-mode oscillations. For the parametric analysis of this phenomenon, a constructive method for stochastic sensitivity and confidence ellipsoids is suggested. It is shown how to simplify this analysis using the principal direction approach. A constructive application of this technique is demonstrated by analyzing the stochastic excitement in the Hodgkin–Huxley model.

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YANG, XIAO-SONG, and QINGDU LI. "A HORSESHOE IN A CELLULAR NEURAL NETWORK OF FOUR-DIMENSIONAL AUTONOMOUS ORDINARY DIFFERENTIAL EQUATIONS." International Journal of Bifurcation and Chaos 17, no. 09 (September 2007): 3211–18. http://dx.doi.org/10.1142/s0218127407018968.

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We obtain numerically a horseshoe in a Poincaré map derived from a cellular neural network described by four-dimensional autonomous ordinary differential equations. Contrary to the horseshoe numerically found in the Hodgkin–Huxley model, which showed evidence that the Poincaré map derived from the Hodgkin–Huxley model has just one expanding direction on some invariant subset, the horseshoe obtained in this paper proves that the Poincaré map derived from the neural network have two expanding directions on some invariant subset.

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Ori, Hillel, Eve Marder, and Shimon Marom. "Cellular function given parametric variation in the Hodgkin and Huxley model of excitability." Proceedings of the National Academy of Sciences 115, no. 35 (August 15, 2018): E8211—E8218. http://dx.doi.org/10.1073/pnas.1808552115.

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How is reliable physiological function maintained in cells despite considerable variability in the values of key parameters of multiple interacting processes that govern that function? Here, we use the classic Hodgkin–Huxley formulation of the squid giant axon action potential to propose a possible approach to this problem. Although the full Hodgkin–Huxley model is very sensitive to fluctuations that independently occur in its many parameters, the outcome is in fact determined by simple combinations of these parameters along two physiological dimensions: structural and kinetic (denoted S and K, respectively). Structural parameters describe the properties of the cell, including its capacitance and the densities of its ion channels. Kinetic parameters are those that describe the opening and closing of the voltage-dependent conductances. The impacts of parametric fluctuations on the dynamics of the system—seemingly complex in the high-dimensional representation of the Hodgkin–Huxley model—are tractable when examined within the S–K plane. We demonstrate that slow inactivation, a ubiquitous activity-dependent feature of ionic channels, is a powerful local homeostatic control mechanism that stabilizes excitability amid changes in structural and kinetic parameters.

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CHUA, LEON, VALERY SBITNEV, and HYONGSUK KIM. "HODGKIN–HUXLEY AXON IS MADE OF MEMRISTORS." International Journal of Bifurcation and Chaos 22, no. 03 (March 2012): 1230011. http://dx.doi.org/10.1142/s021812741230011x.

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This paper presents a rigorous and comprehensive nonlinear circuit-theoretic foundation for the memristive Hodgkin–Huxley Axon Circuit model. We show that the Hodgkin–Huxley Axon comprises a potassium ion-channel memristor and a sodium ion-channel memristor, along with some mundane circuit elements. From this new perspective, many hitherto unresolved anomalous phenomena and paradoxes reported in the literature are explained and clarified. The yet unknown nonlinear dynamical mechanisms which give birth to the action potentials remain hidden within the memristors, and the race is on for uncovering the ultimate truth.

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Cavaterra, Cecilia, Denis Enăchescu, and Gabriela Marinoschi. "Sliding mode control of the Hodgkin–Huxley mathematical model." Evolution Equations & Control Theory 8, no. 4 (2019): 883–902. http://dx.doi.org/10.3934/eect.2019043.

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WANG, J., J. GENG, and X. FEI. "Two-parameters Hopf bifurcation in the Hodgkin–Huxley model." Chaos, Solitons & Fractals 23, no. 3 (February 2005): 973–80. http://dx.doi.org/10.1016/s0960-0779(04)00350-9.

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Baravalle, Roman, Osvaldo A. Rosso, and Fernando Montani. "A path integral approach to the Hodgkin–Huxley model." Physica A: Statistical Mechanics and its Applications 486 (November 2017): 986–99. http://dx.doi.org/10.1016/j.physa.2017.06.016.

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Nagy, A. M., and N. H. Sweilam. "An efficient method for solving fractional Hodgkin–Huxley model." Physics Letters A 378, no. 30-31 (June 2014): 1980–84. http://dx.doi.org/10.1016/j.physleta.2014.06.012.

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Crotty, Patrick, and Thomas Sangrey. "Optimization of battery strengths in the Hodgkin–Huxley model." Neurocomputing 74, no. 18 (November 2011): 3843–54. http://dx.doi.org/10.1016/j.neucom.2011.07.021.

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Yedjour, Hayat, Boudjelal Meftah, Olivier Lézoray, and Abdelkader Benyettou. "Edge detection based on Hodgkin–Huxley neuron model simulation." Cognitive Processing 18, no. 3 (April 3, 2017): 315–23. http://dx.doi.org/10.1007/s10339-017-0803-z.

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Stiles, P. J., and C. G. Gray. "Improved Hodgkin–Huxley type model for neural action potentials." European Biophysics Journal 50, no. 6 (June 28, 2021): 819–28. http://dx.doi.org/10.1007/s00249-021-01547-z.

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Campbell, Kayleigh, Laura Staugler, and Andrea Arnold. "Estimating Time-Varying Applied Current in the Hodgkin-Huxley Model." Applied Sciences 10, no. 2 (January 11, 2020): 550. http://dx.doi.org/10.3390/app10020550.

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The classic Hodgkin-Huxley model is widely used for understanding the electrophysiological dynamics of a single neuron. While applying a low-amplitude constant current to the system results in a single voltage spike, it is possible to produce multiple voltage spikes by applying time-varying currents, which may not be experimentally measurable. The aim of this work is to estimate time-varying applied currents of different deterministic forms given noisy voltage data. In particular, we utilize an augmented ensemble Kalman filter with parameter tracking to estimate four different time-varying applied current parameters and associated Hodgkin-Huxley model states, along with uncertainty bounds in each case. We test the efficiency of the parameter tracking algorithm in this setting by analyzing the effects of changing the standard deviation of the parameter drift and the frequency of data available on the resulting time-varying applied current estimates and related uncertainty.

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Ori, Hillel, Hananel Hazan, Eve Marder, and Shimon Marom. "Dynamic clamp constructed phase diagram for the Hodgkin and Huxley model of excitability." Proceedings of the National Academy of Sciences 117, no. 7 (February 5, 2020): 3575–82. http://dx.doi.org/10.1073/pnas.1916514117.

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Excitability—a threshold-governed transient in transmembrane voltage—is a fundamental physiological process that controls the function of the heart, endocrine, muscles, and neuronal tissues. The 1950s Hodgkin and Huxley explicit formulation provides a mathematical framework for understanding excitability, as the consequence of the properties of voltage-gated sodium and potassium channels. The Hodgkin–Huxley model is more sensitive to parametric variations of protein densities and kinetics than biological systems whose excitability is apparently more robust. It is generally assumed that the model’s sensitivity reflects missing functional relations between its parameters or other components present in biological systems. Here we experimentally assembled excitable membranes using the dynamic clamp and voltage-gated potassium ionic channels (Kv1.3) expressed in Xenopus oocytes. We take advantage of a theoretically derived phase diagram, where the phenomenon of excitability is reduced to two dimensions defined as combinations of the Hodgkin–Huxley model parameters, to examine functional relations in the parameter space. Moreover, we demonstrate activity dependence and hysteretic dynamics over the phase diagram due to the impacts of complex slow inactivation kinetics. The results suggest that maintenance of excitability amid parametric variation is a low-dimensional, physiologically tenable control process. In the context of model construction, the results point to a potentially significant gap between high-dimensional models that capture the full measure of complexity displayed by ion channel function and the lower dimensionality that captures physiological function.

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Zhang, Xiaohong, Zhengze Wu, and Leon Chua. "Hearts are Poised Near the Edge of Chaos." International Journal of Bifurcation and Chaos 30, no. 09 (July 2020): 2030023. http://dx.doi.org/10.1142/s0218127420300232.

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The Cardiac Purkinje Fiber (CPF) is the last branch of the heart conduction system, which is meshed with the normal ventricular myocyte. Purkinje fiber plays a key role in the occurrence of ventricular arrhythmia and maintenance. Does the heart Purkinje fiber cells have the same memory function as the cerebral nerve? In this paper, the cardiac Hodgkin–Huxley equation is taken as the object of study. In particular, we find that the potassium ion-channel [Formula: see text] and the sodium ion-channel [Formula: see text] are memristors. We also derive the small-signal equivalent circuits about the equilibrium points of the CPF Hodgkin–Huxley model. According to the principle of local activity, the regions of Locally-Active domain, Edge of Chaos domain and Locally-Passive domain are partitioned under parameters [Formula: see text], and the domain exhibiting the normal human heartbeat frequency range (Goldilocks Zone) is identified. Meanwhile, the Super-Critical Hopf bifurcation of the CPF Hodgkin–Huxley model is identified. Finally, the migration changes between different state domains under external current [Formula: see text] excitation are analyzed in detail. All of the above complex nonlinear dynamics are distilled and mapped geometrically into a surreal union of intersecting two-dimensional manifolds, dubbed the Hodgkin–Huxley’s magic roof.

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Andreev, Valery, Valerii Ostrovskii, Timur Karimov, Aleksandra Tutueva, Elena Doynikova, and Denis Butusov. "Synthesis and Analysis of the Fixed-Point Hodgkin–Huxley Neuron Model." Electronics 9, no. 3 (March 5, 2020): 434. http://dx.doi.org/10.3390/electronics9030434.

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In many tasks related to realistic neurons and neural network simulation, the performance of desktop computers is nowhere near enough. To overcome this obstacle, researchers are developing FPGA-based simulators that naturally use fixed-point arithmetic. In these implementations, little attention is usually paid to the choice of numerical method for the discretization of the continuous neuron model. In our study, the implementation accuracy of a neuron described by simplified Hodgkin–Huxley equations in fixed-point arithmetic is under investigation. The principle of constructing a fixed-point neuron model with various numerical methods is described. Interspike diagrams and refractory period analysis are used for the experimental study of the synthesized discrete maps of the simplified Hodgkin–Huxley neuron model. We show that the explicit midpoint method is much better suited to simulate the neuron dynamics on an FPGA than the explicit Euler method which is in common use.

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Eikenberry, Steffen E., and Vasilis Z. Marmarelis. "Principal Dynamic Mode Analysis of the Hodgkin–Huxley Equations." International Journal of Neural Systems 25, no. 02 (February 12, 2015): 1550001. http://dx.doi.org/10.1142/s012906571550001x.

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We develop an autoregressive model framework based on the concept of Principal Dynamic Modes (PDMs) for the process of action potential (AP) generation in the excitable neuronal membrane described by the Hodgkin–Huxley (H–H) equations. The model's exogenous input is injected current, and whenever the membrane potential output exceeds a specified threshold, it is fed back as a second input. The PDMs are estimated from the previously developed Nonlinear Autoregressive Volterra (NARV) model, and represent an efficient functional basis for Volterra kernel expansion. The PDM-based model admits a modular representation, consisting of the forward and feedback PDM bases as linear filterbanks for the exogenous and autoregressive inputs, respectively, whose outputs are then fed to a static nonlinearity composed of polynomials operating on the PDM outputs and cross-terms of pair-products of PDM outputs. A two-step procedure for model reduction is performed: first, influential subsets of the forward and feedback PDM bases are identified and selected as the reduced PDM bases. Second, the terms of the static nonlinearity are pruned. The first step reduces model complexity from a total of 65 coefficients to 27, while the second further reduces the model coefficients to only eight. It is demonstrated that the performance cost of model reduction in terms of out-of-sample prediction accuracy is minimal. Unlike the full model, the eight coefficient pruned model can be easily visualized to reveal the essential system components, and thus the data-derived PDM model can yield insight into the underlying system structure and function.

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43

William, Aristizabal Botero, H. Salas Alvaro, and Janeth Gonzalez Colorado Silvia. "The Hodgkin-Huxley neuron model on the fast phase plane." International Journal of Physical Sciences 8, no. 20 (May 30, 2013): 1049–57. http://dx.doi.org/10.5897/ijps11.1334.

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Ostrovskiy, Valeriy, Denis Butusov, Artur Karimov, and Valeriy Andreev. "DISCRETIZATION EFFECTS DURING NUMERICAL INVESTIGATION OF HODGKIN-HUXLEY NEURON MODEL." Bulletin of Bryansk state technical university 2019, no. 12 (December 19, 2019): 94–101. http://dx.doi.org/10.30987/1999-8775-2019-2019-12-94-101.

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Computer design is a valuable tool in the course of designing neuro-morphic systems. In particular it allows investigating basic mechanisms of neuron pulse activities in networks. For computer modeling it is necessary to digitize a continuous model of the system by means of the application of discrete operators able to keep basic properties of a prototype. But the accuracy of discrete models may decrease because of negative effects caused by the type of the method used, by a discretization pitch and errors in rounding off. This fact is significant for the analysis of non-linear systems to which belong the models of biological neurons. As a possible solution of the problem may be the development of specialized tools for the analysis of dynamic systems with the focus upon numerical methods used. In this paper by the example of the modeling of the neuron described by Hodgkin-Huxley classical equations there is considered a set of widespread methods for ODU solution. In the course of investigations there are shown possible negative consequences of incorrect use of some discrete operators. In the paper the results of two sets of computer experiments are presented. The first ones determine the limitations for the practical use of the methods of the first accuracy order during modeling neurons in the mode of resonance generation of action potentials. The second ones show discretization effects connected with chaotic modes of neurons functioning: incorrect behavior of discrete models which is manifested in the emergence of chaotic transition processes. The investigation results may be used at the formation of modeling tool packages both, non-linear dynamic systems in the whole, and neuro-morphic systems in particular.

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Bhatia, Suman, Phool Singh, and Prabha Sharma. "Hodgkin–Huxley model based on ionic transport in axoplasmic fluid." Journal of Integrative Neuroscience 16, no. 4 (February 5, 2018): 401–17. http://dx.doi.org/10.3233/jin-170029.

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46

Meunier, Claude, and Idan Segev. "Playing the Devil's advocate: is the Hodgkin–Huxley model useful?" Trends in Neurosciences 25, no. 11 (November 2002): 558–63. http://dx.doi.org/10.1016/s0166-2236(02)02278-6.

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Wang, Yihong, Rubin Wang, and Xuying Xu. "Neural Energy Supply-Consumption Properties Based on Hodgkin-Huxley Model." Neural Plasticity 2017 (2017): 1–11. http://dx.doi.org/10.1155/2017/6207141.

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Electrical activity is the foundation of the neural system. Coding theories that describe neural electrical activity by the roles of action potential timing or frequency have been thoroughly studied. However, an alternative method to study coding questions is the energy method, which is more global and economical. In this study, we clearly defined and calculated neural energy supply and consumption based on the Hodgkin-Huxley model, during firing action potentials and subthreshold activities using ion-counting and power-integral model. Furthermore, we analyzed energy properties of each ion channel and found that, under the two circumstances, power synchronization of ion channels and energy utilization ratio have significant differences. This is particularly true of the energy utilization ratio, which can rise to above 100% during subthreshold activity, revealing an overdraft property of energy use. These findings demonstrate the distinct status of the energy properties during neuronal firings and subthreshold activities. Meanwhile, after introducing a synapse energy model, this research can be generalized to energy calculation of a neural network. This is potentially important for understanding the relationship between dynamical network activities and cognitive behaviors.

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Telksnys, Tadas, Zenonas Navickas, Inga Timofejeva, Romas Marcinkevicius, and Minvydas Ragulskis. "Symmetry breaking in solitary solutions to the Hodgkin–Huxley model." Nonlinear Dynamics 97, no. 1 (May 16, 2019): 571–82. http://dx.doi.org/10.1007/s11071-019-04998-4.

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Wang, Jiang, Liangquan Chen, and Xianyang Fei. "Analysis and control of the bifurcation of Hodgkin–Huxley model." Chaos, Solitons & Fractals 31, no. 1 (January 2007): 247–56. http://dx.doi.org/10.1016/j.chaos.2005.09.060.

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Eikenberry, Steffen E., and Vasilis Z. Marmarelis. "A nonlinear autoregressive Volterra model of the Hodgkin–Huxley equations." Journal of Computational Neuroscience 34, no. 1 (August 10, 2012): 163–83. http://dx.doi.org/10.1007/s10827-012-0412-x.

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Journal articles on the topic 'Hodgkin-Huxley model'

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