Coupling Dependence on Chaos Synchronization Process in a Network of Rulkov Neurons

Abstract

This paper investigates the impact of network conformation on chaos synchronization in driven complex networks in a master-slave setting. We analyze the control and prediction of complex networks under perturbations. Although chaotic dynamics suppression is well understood in low-dimensional systems, it is not well described in more complex ones. To assess a network’s ability to amplify or suppress disturbances, we track ensembles of possible trajectories in the driven subsystem which give insights into nonlocal convergence properties in a master-slave setting. We demonstrate how the stability of forced networks of Rulkov neurons is dependent on network coupling architecture and how the duration of chaotic transients depends on initial conditions. Furthermore, we find that each network generator algorithm has specific sets of parameters that can lead to stable or nonstable states. Our results indicate that network types are more critical than isolated connections for suppressing chaotic dynamics in driven networks. Finally, we identify that under certain circumstances, the transient period before synchronization correlates with high convergence rates for certain initial conditions. This suggests nonuniform convergence rates in the phase space of driven neural networks.