Generalized synchronization in mutually coupled oscillators and complex networks

TL;DR

This paper introduces a new concept of generalized synchronization applicable to mutually coupled oscillators and complex networks, confirmed through Lyapunov exponents and nearest neighbor methods.

Contribution

It extends the understanding of synchronization to complex topologies and coupled systems, providing new tools for analysis.

Findings

Lyapunov exponents depend on coupling strength

Generalized synchronization verified by nearest neighbor method

Applicable to complex network topologies

Abstract

We introduce a novel concept of generalized synchronization, able to encompass the setting of collective synchronized behavior for mutually coupled systems and networking systems featuring complex topologies in their connections. The onset of the synchronous regime is confirmed by the dependence of the system's Lyapunov exponents on the coupling parameter. The presence of a generalized synchronization regime is verified by means of the nearest neighbor method.