TAILIEUCHUNG - Lyapunov based synchronization of two coupled chaotic hindmarsh rose neurons
This paper addresses the synchronization of coupled chaotic Hindmarsh-Rose neurons. A sufficient condition for self-synchronization is first attained by using Lyapunov method. Also, to achieve the synchronization between two coupled Hindmarsh-Rose neurons when the selfsynchronization condition not satisfied, a Lyapunov-based nonlinear control law is proposed and its asymptotic stability is proved. To verify the effectiveness of the proposed method, numerical simulations are performed. | Journal of Computer Science and Cybernetics, , (2014), 337–348 DOI: LYAPUNOV-BASED SYNCHRONIZATION OF TWO COUPLED CHAOTIC HINDMARSH-ROSE NEURONS LE HOA NGUYEN1 , KEUM-SHIK HONG2 1 Department of Electrical Engineering, Danang University of Science and Technology-The University of Danang; nglehoa@ 2 Department of Cogno-Mechatronics Engineering and School of Mechanical Engineering, Pusan National University; kshong@ Abstract. This paper addresses the synchronization of coupled chaotic Hindmarsh-Rose neurons. A sufficient condition for self-synchronization is first attained by using Lyapunov method. Also, to achieve the synchronization between two coupled Hindmarsh-Rose neurons when the selfsynchronization condition not satisfied, a Lyapunov-based nonlinear control law is proposed and its asymptotic stability is proved. To verify the effectiveness of the proposed method, numerical simulations are performed. Keywords. Chaos, Hindmarsh-Rose neurons, Lyapunov function, nonlinear control, synchronization. 1. INTRODUCTION Neurons play an important role in processing the information in the brain. To understand the behaviour of individual neurons and further comprehend the biological information processing of neural networks, various neuronal models have been proposed [1–4]. One of the most important models is the Hodgkin-Huxley model [1]. This model describes how action potentials are initiated and propagated in the squid giant axon in term of time- and voltage-dependent conductance of sodium and potassium. However, the Hodgkin-Huxley model consists of a large number of nonlinear equations as well as parameters that makes it difficult to study the behaviour of neuronal networks. The Hindmarsh-Rose (HR) model, a simplification of the Hodgkin-Huxley and the Fitzhugh models, provides very realistic descriptions on various dynamic features of biological neurons such as rapid firing, bursting, and adaptation [4]. Therefore, the
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