Synchronization of coupled chaotic Hindmarsh Rose neurons: An adaptive approach**Project supported by the Beijing Natural Science Foundation, China (Grant No. 4132005), the National Natural Science Foundation of China (Grant No. 61403006), the Importation and Development of High-Caliber Talent Project of Beijing Municipal Institutions, China (Grant No. YETP1449), and the Project of Scientific and Technological Innovation Platform, China (Grant No. PXM2015_014213_000063).

Abstract

In this paper, we consider the synchronization of chaotic Hindmarsh Rose (HR) neurons via a scalar control input. Chaotic HR neurons coupled with a gap junction are taken into consideration, and an active compensation mechanism-based adaptive control is employed to realize the synchronization of two HR neurons. As such an adaptive control is utilized, an accurate model of the system is of no necessity. Asymptotical synchronization of two HR neurons is guaranteed by theoretical results. Numerical results are also provided to confirm the proposed synchronization approach.