Stability and synchronization of coupled Rulkov map-based neurons with chemical synapses

摘要

The stability and synchronization analysis of two chaotic Rulkov maps coupled by bidirectional and symmetric chemical synapses are taken into account. As a function of intrinsic control parameters alpha, sigma, eta, reversal potential v, synaptic parameters theta, k, and external chemical coupling strength g(c), conditions for stability of a fixed point for this system are derived. Some typical domains are chosen for numerical simulations which include time evolution of transmembrane voltages and phase portraits, and both of them are presented for theoretical analysis. Based on the master stability functions approach and calculation of the maximum Lyapunov exponents of synchronization errors, synchronized regions of the coupled neurons and a strip-shaped chaotic structure in parameter-space are obtained. Specially, given some values of control parameter alpha, we propose interval ranges of coupling strength g(c) in which the two chaotic Rulkov map-based neurons can be synchronized completely. It is shown that there exist different transition mechanisms of the neuronal spiking and bursting synchronization. The synchronized regions will become smaller and smaller as control parameter alpha or synaptic parameter theta increases. Nevertheless, the coupled neurons can at first transit from desynchrony to in-phase synchronization, and then to complete synchronization as chemical coupling strength g(c) increases. Compared with control parameter alpha and synaptic parameter theta, chemical coupling strength g(c) plays an opposite role in the process of synchronization transition. These findings could be useful for further understanding the role of two chaotic Rulkov maps coupled by bidirectional and symmetric chemical synapses in the field of cooperative behaviors of coupled neurons. (C) 2015 Elsevier B.V. All rights reserved.