Enhancing synchronization in chaotic oscillators by induced heterogeneity

TL;DR

This paper demonstrates that introducing heterogeneity in an intermediate relay oscillator can enhance synchronization among identical chaotic oscillators, reducing the coupling needed for synchronization across various network configurations.

Contribution

The study reveals that heterogeneity in a relay oscillator can facilitate synchronization in chaotic systems, a novel approach to controlling chaos in complex networks.

Findings

Heterogeneity reduces the critical coupling for synchronization.

Common lag synchronization emerges between relay and oscillators.

Enhancing effect observed in various network topologies.

Abstract

We report enhancing of complete synchronization in identical chaotic oscillators when their interaction is mediated by a mismatched oscillator. The identical oscillators now interact indirectly through the intermediate relay oscillator. The induced heterogeneity in the intermediate oscillator plays a constructive role in reducing the critical coupling for a transition to complete synchronization. A common lag synchronization emerges between the mismatched relay oscillator and its neighboring identical oscillators that leads to this enhancing effect. We present examples of one-dimensional open array, a ring, a star network and a two-dimensional lattice of dynamical systems to demonstrate how this enhancing effect occurs. The paradigmatic R\"ossler oscillator is used as a dynamical unit, in our numerical experiment, for different networks to reveal the enhancing phenomenon.