Dynamics of Hindmarsh–Rose neurons connected via adaptive memristive synapse

Abstract

Experimental data suggest that temporal neural activity regulates the synaptic weight, a phenomenon known as activity-dependent synaptic plasticity. Thus far, a diversity of neuronal learning rules have been adopted; a likely one is a Hebbian adaptation based on neuron synchrony. Regarding the growing appeal for coupling neurons through memristors, an element bridging magnetic flux and ion exchange, the existing literature on adapting memristive synapses seems limited. This paper aims to investigate two Hindmarsh–Rose neurons coupled through an adaptive memristor synapse by treating adaptive coupling parameters as bifurcation parameters. The capability of adaptive memristive coupling to generate high periodic and chaotic oscillations in the intrinsic periodic behavior of HR neurons is revealed. Synchronization analysis suggests that bifurcation scenarios are closely associated with the transition of the generic firings of two neurons from asynchrony to perfect synchrony. The Hamilton energy analysis indicates that as two neurons transition to synchrony, their energy levels equalize, and the energy fluctuations within the memristive coupling channel diminish. The value of the adaption parameter by which neurons synchronize also depends on the intrinsic parameters of HR, particularly the one associated with the effectiveness of slow channels. Additionally, the synchronization's robustness against different noise intensities has been examined. At last, on the matter of multistability, several pieces of evidence also exist.