摘要： •We study the nonlinearly coupled Hindmarsh–Rose neurons with a sigmoid coupling function.•We show that the nonlinearly coupled system is eventually dissipative.•We derive eigenvalue-related criteria to ensure the global exponential synchronization.•Numerical experiments for the modular network with or without the small-world property are presented. In this paper, we study the asymptotic collective behavior of nonlinearly coupled dynamical network of Hindmarsh–Rose neurons, where the neurons are asymmetrically interconnected through a sigmoidal coupling function. We first show that the nonlinearly coupled dynamical network with a certain asymmetric connection topology is eventually dissipative and hence all solutions are eventually bounded. Furthermore, under some mild conditions on the system parameters, we derive an eigenvalue-related criterion that ensures the nonlinearly coupled dynamical network to be globally exponentially synchronized. Numerical experiments for the modular network of Hindmarsh–Rose neurons with or without the small-world property are given to demonstrate the theoretical results. 出版者： Elsevier Inc 出版日期： 2015-11-01 出處： Applied mathematical modelling, 2015-11, Vol.39 (21), p.6631-6644 資源來源： ScienceDirect - Freedom Collection 版權： 2015 Elsevier Inc. 識別號： ISSN: 0307-904X 識別號： DOI: 10.1016/j.apm.2015.02.017
