Synchronization of coupled chaotic FitzHugh–Nagumo systems

• Published in: Communications in nonlinear science & numerical simulation 2012-04, Vol.17 (4), p.1615-1627
• Main Authors: Aqil, Muhammad, Hong, Keum-Shik, Jeong, Myung-Yung
• Format: Article
• Language: English
• Subjects: Asymptotic properties; Chaos synchronization; Disturbances; Dynamical systems; External electrical stimulation (EES); FitzHugh–Nagumo (FHN) equations; Linear matrix inequality (LMI); Mathematical models; Nonlinear dynamics; Stability; Synchronism; Synchronization; Uniform ultimate boundedness (UUB)
• ISSN: 1007-5704; 1878-7274
• DOI: 10.1016/j.cnsns.2011.09.028

► Simple single- and two-input control to synchronize locally Lipschitz FHN systems. ► Local asymptotic stability with states boundedness. ► Locally uniformly ultimately bounded stability in the presence of disturbances. ► Robustness against disturbances, bound to which is related with control parameters. ► Simplified selection of control parameters and constraint matrices using LMI tools. This paper addresses dynamic synchronization of two FitzHugh–Nagumo (FHN) systems coupled with gap junctions. All the states of the coupled chaotic system, treating either as single-input or two-input control system, are synchronized by stabilizing their error dynamics, using simplest and locally robust control laws. The local asymptotic stability, chosen by utilizing the local Lipschitz nonlinear property of the model to address additionally the non-failure of the achieved synchronization, is ensured by formulating the matrix inequalities on the basis of Lyapunov stability theory. In the presence of disturbances, it ensures the local uniform ultimate boundedness. Furthermore, the robustness of the proposed methods is ensured against bounded disturbances besides providing the upper bound on disturbances. To the best of our knowledge, this is the computationally simplest solution for synchronization of coupled FHN modeled systems along with unique advantages of less conservative local asymptotic stability of synchronization errors with robustness. Numerical simulations are carried out to successfully validate the proposed control strategies.