Master-slave synchronization criteria for chaotic hindmarsh-rose neurons using linear feedback control

This article is concerned with master–slave synchronization for two chaotic Hindmarsh–Rose neurons. The main contribution of this article is that three synchronization criteria are derived by using linear feedback control without the estimation of bounds of state variables of controlled slave neurons. Three simulation examples are used to illustrate the effectiveness of our results. © 2015 Wiley Periodicals, Inc. Complexity, 2015

[1]  Zidong Wang,et al.  Synchronization and State Estimation for Discrete-Time Complex Networks With Distributed Delays , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[2]  Jinde Cao,et al.  Cluster synchronization in an array of hybrid coupled neural networks with delay , 2009, Neural Networks.

[3]  Xiang Li,et al.  Pinning a complex dynamical network to its equilibrium , 2004, IEEE Trans. Circuits Syst. I Regul. Pap..

[4]  Guanrong Chen,et al.  A time-varying complex dynamical network model and its controlled synchronization criteria , 2004, IEEE Trans. Autom. Control..

[5]  Jinde Cao,et al.  Synchronization Error Estimation and Controller Design for Delayed Lur'e Systems With Parameter Mismatches , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[6]  Xiang Li,et al.  Phase synchronization in complex networks with decayed long-range interactions , 2006 .

[7]  Jianping Cai,et al.  Robust synchronization of chaotic horizontal platform systems with phase difference , 2007 .

[8]  Bin Deng,et al.  Chaos synchronization of coupled neurons via adaptive sliding mode control , 2011 .

[9]  Arun V. Holden,et al.  Bifurcations, burstings, chaos and crises in the Rose-Hindmarsh model for neuronal activity , 1993 .

[10]  Zhimin He,et al.  Bifurcations and chaos in a two-dimensional discrete Hindmarsh–Rose model , 2014 .

[11]  Xiaoyi Ma,et al.  No-chattering sliding mode control chaos in Hindmarsh-Rose neurons with uncertain parameters , 2011, Comput. Math. Appl..

[12]  Guanrong Chen,et al.  Chaos synchronization of coupled neurons with gap junctions , 2006 .

[13]  Xuerong Shi,et al.  Lag synchronization of two identical Hindmarsh-Rose neuron systems with mismatched parameters and external disturbance via a single sliding mode controller , 2012, Appl. Math. Comput..

[14]  Arun V. Holden,et al.  From simple to complex oscillatory behaviour via intermittent chaos in the Rose-Hindmarsh model for neuronal activity , 1992 .

[15]  Zidong Wang,et al.  Stability and Synchronization of Discrete-Time Markovian Jumping Neural Networks With Mixed Mode-Dependent Time Delays , 2009, IEEE Transactions on Neural Networks.

[16]  Arun V. Holden,et al.  Crisis-induced chaos in the Rose-Hindmarsh model for neuronal activity , 1992 .

[17]  J. Lisman Bursts as a unit of neural information: making unreliable synapses reliable , 1997, Trends in Neurosciences.

[18]  Xinghuo Yu,et al.  Generating 3-D multi-scroll chaotic attractors: A hysteresis series switching method , 2004, Autom..

[19]  Marco Righero,et al.  Synchronization in Networks of Hindmarsh–Rose Neurons , 2008, IEEE Transactions on Circuits and Systems II: Express Briefs.

[20]  Sohrab Effati,et al.  Ultimate bound sets of a hyperchaotic system and its application in chaos synchronization , 2015, Complex..

[21]  Shenquan Liu,et al.  Codimension-two bifurcation analysis in two-dimensional Hindmarsh–Rose model , 2012 .

[22]  Abdesselem Boulkroune,et al.  Adaptive fuzzy control-based projective synchronization of uncertain nonaffine chaotic systems , 2015, Complex..

[23]  SuHongye,et al.  Exponential state estimation for discrete-time switched genetic regulatory networks with random delays , 2014 .

[24]  B. Connors,et al.  Intrinsic oscillations of neocortex generated by layer 5 pyramidal neurons. , 1991, Science.

[25]  Jinde Cao,et al.  Local Synchronization of a Complex Network Model , 2009, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[26]  Alessandro Chiuso,et al.  Numerical conditioning and asymptotic variance of subspace estimates , 2004, Autom..

[27]  Hongli Li,et al.  Impulsive synchronization of time delay bursting neuron systems with unidirectional coupling , 2015, Complex..

[28]  Ju H. Park,et al.  Exponential synchronization for fractional-order chaotic systems with mixed uncertainties , 2015, Complex..

[29]  Le Hoa Nguyen,et al.  Adaptive synchronization of two coupled chaotic Hindmarsh-Rose neurons by controlling the membrane potential of a slave neuron , 2013 .

[30]  Ju H. Park,et al.  Robust mixed H∞ and passive filtering for networked Markov jump systems with impulses , 2014, Signal Process..

[31]  J. Hindmarsh,et al.  A model of neuronal bursting using three coupled first order differential equations , 1984, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[32]  Mohammad Shahzad,et al.  Global chaos synchronization of new chaotic system using linear active control , 2015, Complex..

[33]  Rathinasamy Sakthivel,et al.  Robust state estimation for discrete-time genetic regulatory networks with randomly occurring uncertainties , 2013 .

[34]  J. Hindmarsh,et al.  A model of the nerve impulse using two first-order differential equations , 1982, Nature.

[35]  Long Huang,et al.  Parameters estimation, mixed synchronization, and antisynchronization in chaotic systems , 2014, Complex..

[36]  Arun V. Holden,et al.  From simple to simple bursting oscillatory behaviour via chaos in the Rose-Hindmarsh model for neuronal activity , 1992 .

[37]  Zidong Wang,et al.  Synchronization of Coupled Neutral-Type Neural Networks With Jumping-Mode-Dependent Discrete and Unbounded Distributed Delays , 2013, IEEE Transactions on Cybernetics.

[38]  Jianping Cai,et al.  Chaos Synchronization Criteria and Costs of Sinusoidally Coupled Horizontal Platform Systems , 2007 .

[39]  Jinde Cao,et al.  Lag Quasi-Synchronization of Coupled Delayed Systems With Parameter Mismatch , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[40]  Le Hoa Nguyen,et al.  Synchronization of coupled chaotic FitzHugh-Nagumo neurons via Lyapunov functions , 2011, Math. Comput. Simul..