Synchronization and chimeras in asymmetrically coupled memristive Tabu learning neuron network

Abstract

The coupling between neuronal oscillators plays an intriguing role in understanding the dynamics of the biological neurons present in realistic situations. Importantly, when the coupling between these neurons assumes an asymmetric nature, it can lead to profound changes in their overall behavior. In order to explore the impact of asymmetrical coupling on neuron models subjected to magnetic flux induction, we employ a coupled Tabu learning neuron model. Specifically, we illustrate the interplay between flux coupling and asymmetric electrical synapses concerning the control parameters of the proposed system using phase portraits, time series, bifurcation analysis, and Lyapunov spectrum. In particular, we show the dynamics by taking into account asymmetric interactions between neurons, from a simple network of two coupled systems to a network of nodes. Primarily, we demonstrate that two coupled systems exhibit synchronization for a fixed magnitude of control parameter with increasing coupling strength. Furthermore, we discuss the collective dynamics for the distinct network connectivity including regular, small-world and random. For all network connections, an increase in coupling strength facilitates a transition from desynchronization to synchronization via chimera state. We believe that attaining synchronization in Tabu learning neuron can act as a pivotal factor for neuron activity, contributing to the realization of such behavior in the context of numerous cognitive processes.