Chimera states in ring-star network of Chua circuits

TL;DR

This paper explores how adding a central node to a ring network of Chua circuits creates chimera states and allows control over frequency domains through radial coupling strength, with implications for system synchronization and control.

Contribution

It demonstrates the emergence of amplitude and frequency chimera states in ring-star networks of Chua circuits and shows how the central node influences frequency domain transitions.

Findings

Radial coupling strength acts as an order parameter for frequency transition.

Chimera states are prevalent in the transition region between frequency domains.

Star connectivity enables frequency control without modifying individual oscillator parameters.

Abstract

We investigate the emergence of amplitude and frequency chimera states in ring-star networks consisting of identical Chua circuits connected via nonlocal diffusive, bidirectional coupling. We first identify single-well chimera patterns in a ring network under nonlocal coupling schemes. When a central node is added to the network, forming a ring-star network, the central node acts as the distributor of information, increasing the chances of synchronization. Numerical simulations show that the radial coupling strength $k$ between the central and the peripheral nodes acts as an order parameter leading from a lower to a higher frequency domain. The transition between the domains takes place for intermediate coupling values, $0.5 <k< 2$, where the frequency chimera states prevail. The transition region (width and boundaries) depends on the Chua oscillator parameters and the network specifics. Potential applications of star connectivity can be found in the control of Chua networks and in other coupled chaotic dynamical systems. By adding one central node and without further modifications to the individual network parameters it is possible to entrain the system to lower or higher frequency domains as desired by the particular applications.