Inducing chimera-synchronization in symmetric complex networks

TL;DR

This paper introduces a control method using pinning coupling to induce chimera-synchronization states in symmetric complex networks of chaotic oscillators, overcoming topological and coupling limitations.

Contribution

It proposes a novel pinning control strategy that guarantees the induction of chimera-synchronization states in symmetric complex networks.

Findings

Successful induction of chimera states via pinning control.

Mathematical proof of critical pinning strength for stability.

Numerical validation on artificial and real-world networks.

Abstract

In a recent study of chaos synchronization in symmetric complex networks [Pecora \textit{et al}., Nat. Commun. {\bf 5}, 4079 (2014)], it is found that stable synchronous clusters may coexist with many non-synchronous nodes in the asynchronous regime, resembling the chimera state observed in regular networks of non-locally coupled periodic oscillators. Although of practical significance, this new type of state, namely the chimera-synchronization state, is hardly generated for the general complex networks, due to either the topological instabilities or the weak coupling strength. Here, based on the strategy of pinning coupling, we propose an effective method for inducing chimera-synchronization in symmetric complex network of coupled chaotic oscillators. We are able to argue mathematically that, by pinning a group of nodes satisfying permutation symmetry, there always exits a critical pinning strength beyond which the unstable chimera-synchronization states can be successfully induced. The feasibility and efficiency of the control method are verified by numerical simulations of both artificial and real-world complex networks, with the numerical results well fitted by the theoretical predictions.