A Nonlinear Synchronization Scheme for （一个非线性同步方案）.pdfVIP

Journal of Electrical Engineering Technology Vol. 5, No. 1, pp. 163~170, 2010 163 A Nonlinear Synchronization Scheme for Hindmarsh-Rose Models † Jung-Su Kim and Frank Allgower* Abstract – Multiple subsystems are required to behave synchronously or cooperatively in many areas. For example, synchronous behaviors are common in networks of (electro-) mechanical systems, cell biology, coupled neurons, and cooperating robots. This paper presents a feedback scheme for synchro- nization between Hindmarsh-Rose models which have polynomial vector fields. We show that the problem is equivalent to finding an asymptotically stabilizing control for error dynamics which is also a polynomial system. Then, an extension to a nonlinear observer-based scheme is presented, which re- duces the amount of information exchange between models. Keywords: Synchronization, Polynomial systems, Nonlinear observer and control 1. Introduction bursting, is particularly important in studying detailed in- teractions in networks containing small number of neurons. Synchronization can be considered as the asymptotic co- In this paper, to solve the synthesis problem for synchroni- incidence of the state vectors of two (or more) systems [5]. zation of polynomial systems, we discuss how to design a Recently, synchronization phenomena among multiple coupling function for synchronization between two H