Adaptive Synchronization of the Identical FitzHugh-Nagumo Chaotic Neuron Models

Chaos is an important applied area in nonlinear dynamical systems and it is applicable to many real-world systems including the biological systems. Nerve membranes are known to exhibit their own nonlinear dynamics which generate and propagate action potentials. Such nonlinear dynamics in nerve membranes can produce chaos in neurons and related bifurcations. In 1952, A.L. Hodgkin and A.F. Huxley proposed a nonlinear dynamical system as a mathematical

[1]  Sundarapandian Vaidyanathan,et al.  Dynamics and Control of Brusselator Chemical Reaction , 2015 .

[2]  Sundarapandian Vaidyanathan Lotka-Volterra Population Biology Models with Negative Feedback and their Ecological Monitoring , 2015 .

[3]  Sundarapandian Vaidyanathan,et al.  Analysis, adaptive control and synchronization of a novel 4-D hyperchaotic hyperjerk system and its SPICE implementation , 2015 .

[4]  Sundarapandian Vaidyanathan,et al.  An Eight - Term Novel Four - Scroll Chaotic System with Cubic Nonlinearity and its Circuit Simulation , 2015 .

[5]  Sundarapandian Vaidyanathan,et al.  Anti-synchronization of four-wing chaotic systems via sliding mode control , 2012, Int. J. Autom. Comput..

[6]  Sundarapandian Vaidyanathan,et al.  Hidden attractors in a chaotic system with an exponential nonlinear term , 2015 .

[7]  Sundarapandian Vaidyanathan,et al.  Hybrid Synchronization of Hyperchaotic Qi and Lü Systems by Nonlinear Control , 2011 .

[8]  Sundarapandian Vaidyanathan,et al.  Hyperchaos, adaptive control and synchronization of a novel 5-D hyperchaotic system with three positive Lyapunov exponents and its SPICE implementation , 2014 .

[9]  Sundarapandian Vaidyanathan,et al.  Analysis, Control and Synchronization of a Nine-Term 3-D Novel Chaotic System , 2015, Chaos Modeling and Control Systems Design.

[10]  Sundarapandian Vaidyanathan,et al.  A 5-D hyperchaotic Rikitake dynamo system with hidden attractors , 2015 .

[11]  S. Vaidyanathan A 3 - D Novel Highly Chaotic System with Four Quadratic Nonlinearities, its Adaptive Control and Anti - Synchronization with Unknown Parameters , 2015 .

[12]  Sundarapandian Vaidyanathan,et al.  Memristor: A New Concept in Synchronization of Coupled Neuromorphic C ircuits , 2015 .

[13]  Sundarapandian Vaidyanathan,et al.  Output Regulation of the Unified Chaotic System , 2011 .

[14]  Sundarapandian Vaidyanathan,et al.  Output Regulation of Arneodo-Coullet Chaotic System , 2011 .

[15]  R. FitzHugh Impulses and Physiological States in Theoretical Models of Nerve Membrane. , 1961, Biophysical journal.

[16]  Sundarapandian Vaidyanathan,et al.  Computational Intelligence Applications in Modeling and Control , 2015, Computational Intelligence Applications in Modeling and Control.

[17]  Sundarapandian Vaidyanathan,et al.  Generalized projective synchronization of Elhadj chaotic systems via adaptive control , 2013, 2013 International Conference on Green Computing, Communication and Conservation of Energy (ICGCE).

[18]  Sundarapandian Vaidyanathan,et al.  Design and SPICE implementation of a 12-term novel hyperchaotic system and its synchronisation via active control , 2015, Int. J. Model. Identif. Control..

[19]  Sundarapandian Vaidyanathan,et al.  ACTIVE CONTROLLER DESIGN FOR THE GENERALIZED PROJECTIVE SYNCHRONIZATION OF THREE -SCROLL CHAOTIC SYSTEMS , 2012 .

[20]  O. Rössler An equation for continuous chaos , 1976 .

[21]  Sundarapandian Vaidyanathan,et al.  The Design of Active Feedback Controllers for the Generalized Projective Synchronization of Hyperchaotic Qi and Hyperchaotic Lorenz Systems , 2011, CISIM.

[22]  Sundarapandian Vaidyanathan Global chaos synchronisation of identical Li-Wu chaotic systems via sliding mode control , 2014, Int. J. Model. Identif. Control..

[23]  Sundarapandian Vaidyanathan,et al.  Adaptive Chaotic Synchronization of Enzymes-Substrates System with Ferroelectric Behaviour in Brain Waves , 2015 .

[24]  Sundarapandian Vaidyanathan,et al.  Global Chaos Synchronization of WINDMI and Coullet Chaotic Systems using Adaptive Backstepping Control Design , 2014 .

[25]  Sundarapandian Vaidyanathan,et al.  Analysis and adaptive synchronization of eight-term 3-D polynomial chaotic systems with three quadratic nonlinearities , 2014 .

[26]  Guoliang Cai,et al.  Chaos Synchronization of a New Chaotic System via Nonlinear Control , 2007 .

[27]  A. Hodgkin,et al.  A quantitative description of membrane current and its application to conduction and excitation in nerve , 1952, The Journal of physiology.

[28]  Sundarapandian Vaidyanathan,et al.  Hybrid Synchronization of Identical Chaotic Systems Using Sliding Mode Control and an Application to Vaidyanathan Chaotic Systems , 2015, Advances and Applications in Sliding Mode Control Systems.

[29]  Sundarapandian Vaidyanathan,et al.  Analysis, Adaptive Control and Synchronization of a Seven - Term Novel 3 - D Chaotic System with Three Quadratic Nonlinearities and its Digital Implementation in LabVIEW , 2015 .

[30]  Rajagopal Karthikeyan,et al.  Hybrid Chaos Synchronization of Four–Scroll Systems via Active Control , 2014 .

[31]  Sundarapandian Vaidyanathan,et al.  Synchronization of Tokamak Systems with Symmetric and Magnetically Confined Plasma via Adaptive Control , 2015 .

[32]  Chuandong Li,et al.  Chaos control and synchronization via a novel chatter free sliding mode control strategy , 2011, Neurocomputing.

[33]  Sundarapandian Vaidyanathan,et al.  A nalysis, Adaptive Control and Anti - Synchronization of a Six - Term Novel Jerk Chaotic System with two Exponential Nonlinearities and its Circuit Simulation , 2015 .

[34]  Sundarapandian Vaidyanathan,et al.  Analysis , Adaptive Control and Adaptive Synchronization of a Nine - Term Novel 3 - D Chaotic System with Four Quadratic Nonlinearities and its Circuit Simulation , 2015 .

[35]  Dominique M. Durand,et al.  Phase synchronization in two coupled chaotic neurons , 1999 .

[36]  V. Sundarapan,et al.  Generalized Projective Synchronization of Two-Scroll Systems via Adaptive Control , 2012 .

[37]  Sundarapandian Vaidyanathan,et al.  Global Chaos Synchronization of Hyperchaotic Lorenz Systems by Sliding Mode Control , 2011 .

[38]  Sundarapandian Vaidyanathan,et al.  Hybrid Synchronization of Hyperchaotic Wang-Chen and Hyperchaotic Lorenz Systems by Active Non-linear Control , 2011 .

[39]  Sundarapandian Vaidyanathan,et al.  Analysis and adaptive control of a novel 3-D conservative no-equilibrium chaotic system , 2015 .

[40]  Sundarapandian Vaidyanathan,et al.  Adaptive Controller and Synchronizer Design for the Qi-Chen Chaotic System , 2012 .

[41]  Sundarapandian Vaidyanathan,et al.  Generalized Projective Synchronization of Double-Scroll Chaotic Systems Using Active Feedback Control , 2012 .

[42]  Sundarapandian Vaidyanathan Generalised projective synchronisation of novel 3-D chaotic systems with an exponential non-linearity via active and adaptive control , 2014, Int. J. Model. Identif. Control..

[43]  Teh-Lu Liao,et al.  Adaptive Chaos Synchronization of FitzHugh-Nagumo Neurons , 2007 .

[44]  Sundarapandian Vaidyanathan,et al.  Adaptive Synchronization of Chemical Chaotic Reactors , 2015 .

[45]  V. Sundarapandian,et al.  Analysis and Anti-Synchronization of a Novel Chaotic System via Active and Adaptive Controllers , 2013 .

[46]  Sundarapandian Vaidyanathan,et al.  Backstepping Controller Design for the Global Chaos Synchronization of Sprott's Jerk Systems , 2015, Chaos Modeling and Control Systems Design.

[47]  Vaidyanathan Sundarapandian,et al.  Adaptive Control and Synchronization Design for the Lu-Xiao Chaotic System , 2013 .

[48]  Sundarapandian Vaidyanathan,et al.  Hybrid synchronization of n–scroll Chua and Lur’e chaotic systems via backstepping control with novel feedback , 2012 .

[49]  Sundarapandian Vaidyanathan,et al.  Global chaos synchronisation of identical chaotic systems via novel sliding mode control method and its application to Zhu system , 2015, Int. J. Model. Identif. Control..

[50]  E. Lorenz Deterministic nonperiodic flow , 1963 .

[51]  Sundarapandian Vaidyanathan,et al.  Analysis, Control and Synchronization of Hyperchaotic Zhou System via Adaptive Control , 2012, ACITY.

[52]  M. T. Yassen,et al.  Chaos synchronization between two different chaotic systems using active control , 2005 .

[53]  Guanrong Chen,et al.  YET ANOTHER CHAOTIC ATTRACTOR , 1999 .

[54]  Sundarapandian Vaidyanathan Analysis, control and synchronisation of a six-term novel chaotic system with three quadratic nonlinearities , 2014, Int. J. Model. Identif. Control..

[55]  Sundarapandian Vaidyanathan,et al.  Hybrid Synchronization of Hyperchaotic Chen Systems via Sliding Mode Control , 2012 .

[56]  Sundarapandian Vaidyanathan,et al.  Adaptive backstepping control, synchronization and circuit simulation of a 3-D novel jerk chaotic system with two hyperbolic sinusoidal nonlinearities , 2014 .

[57]  P. Sarasu,et al.  The Generalized Projective Synchronization of Hyperchaotic Lorenz and Hyperchaotic Qi Systems via Active Control , 2011 .

[58]  Sundarapandian Vaidyanathan,et al.  Anti-synchronization of Identical Chaotic Systems Using Sliding Mode Control and an Application to Vaidyanathan-Madhavan Chaotic Systems , 2015, Advances and Applications in Sliding Mode Control Systems.

[59]  Sundarapandian Vaidyanathan,et al.  Analysis, Control, Synchronization and SPICE Implementation of a Novel 4 - D Hyperchaotic Rikitake Dynamo System without Equilibrium , 2015 .

[60]  S. Yoshizawa,et al.  An Active Pulse Transmission Line Simulating Nerve Axon , 1962, Proceedings of the IRE.

[61]  V. Sundarapan,et al.  Hybrid Synchronization of Hyperchaotic Lorenz and Hyperchaotic Chen Systems via Active Control , 2012 .

[62]  Sundarapandian Vaidyanathan,et al.  Global Chaos Synchronization of Hyperchaotic Bao and Xu Systems by Active Nonlinear Control , 2011 .

[63]  Sundarapandian Vaidyanathan,et al.  Global Chaos Synchronization of Lü and Pan Systems by Adaptive Nonlinear Control , 2011 .

[64]  Alain Arneodo,et al.  Possible new strange attractors with spiral structure , 1981 .

[65]  S. Vaidyanathan Analysis and Adaptive Synchronization of Two Novel Chaotic Systems with Hyperboli c Sinusoidal and Cosinusoidal Nonlinearity and Unknown Parameters , 2013 .

[66]  V. Sundarapandian,et al.  Analysis, control, synchronization, and circuit design of a novel chaotic system , 2012, Math. Comput. Model..

[67]  Sundarapandian Vaidyanathan,et al.  Sliding Mode Controller Design for the Global Chaos Synchronization of Coullet Systems , 2012 .

[68]  Tao Wang,et al.  Chaos control and hybrid projective synchronization for a class of new chaotic systems , 2011, Comput. Math. Appl..

[69]  Sundarapandian Vaidyanathan,et al.  Multi-scroll Chaotic Oscillator Based on a First-Order Delay Differential Equation , 2015, Chaos Modeling and Control Systems Design.

[70]  Sundarapandian Vaidyanathan,et al.  Hybrid Synchronization of n-scroll Chaotic Chua Circuits using Adaptive Backstepping Control Design with Recursive Feedback , 2013 .

[71]  S. Vaidyanathan,et al.  A 3 - D Novel Conservative Chaotic System and its Generalized Projective Synchronization via Adaptive Control , 2015 .

[72]  Sundarapandian Vaidyanathan,et al.  Analysis, properties and control of an eight-term 3-D chaotic system with an exponential nonlinearity , 2015, Int. J. Model. Identif. Control..

[73]  J. Sprott,et al.  Some simple chaotic flows. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[74]  Sundarapandian Vaidyanathan,et al.  Hyperchaos, qualitative analysis, control and synchronisation of a ten-term 4-D hyperchaotic system with an exponential nonlinearity and three quadratic nonlinearities , 2015, Int. J. Model. Identif. Control..

[75]  Sundarapandian Vaidyanathan,et al.  A Memristor-Based Hyperchaotic System with Hidden Attractors: Dynamics, Synchronization and Circuital Emulating , 2015 .

[76]  V. Sundarapan,et al.  Adaptive Anti-Synchronization of Uncertain Tigan and Li Systems , 2012 .

[77]  Sundarapandian Vaidyanathan,et al.  Generalized Projective Synchronization of Three-Scroll Chaotic Systems via Active Control , 2012 .

[78]  Sundarapandian Vaidyanathan,et al.  Analysis and Control of a 4-D Novel Hyperchaotic System , 2015, Chaos Modeling and Control Systems Design.

[79]  Sundarapandian Vaidyanathan,et al.  Synchronization Phenomena in Coupled Colpitts Circuits , 2015 .

[80]  Sundarapandian Vaidyanathan,et al.  Global Chaos Synchronization of Hyperchaotic Pang and Hyperchaotic Wang Systems via Adaptive Control , 2011 .

[81]  Sundarapandian Vaidyanathan,et al.  Global Chaos Synchronization of n-Scroll Chua Circuit and Lur’e System using Backstepping Control Design with Recursive Feedback , 2014 .

[82]  Sundarapandian Vaidyanathan,et al.  Analysis, synchronization and circuit design of a novel butterfly attractor , 2014 .

[83]  Sundarapandian Vaidyanathan,et al.  Hybrid Chaos Synchronization of Liu and Lü Systems by Active Nonlinear Control , 2011, CSE 2011.

[84]  Sundarapandian Vaidyanathan,et al.  Anti-synchronization of Li and T Chaotic Systems by Active Nonlinear Control , 2011 .

[85]  Sundarapandian Vaidyanathan,et al.  Chaos Modeling and Control Systems Design , 2014, Chaos Modeling and Control Systems Design.

[86]  Sundarapandian Vaidyanathan,et al.  Adaptive Backstepping Controller Design for the Anti - Synchronization of Identical WINDMI Chaotic Systems with Unknown Parameters and its SPICE Implementation , 2015 .

[87]  Jinhu Lu,et al.  A New Chaotic Attractor Coined , 2002, Int. J. Bifurc. Chaos.