Synchronization of Two Diffusively Coupled Chaotic Parametrically Excited nonidentical Pendula

TL;DR

This paper demonstrates that multiple analytical methods are necessary to accurately detect synchronization in coupled non-identical chaotic pendula, revealing an almost synchronization state achieved through frequency entrainment.

Contribution

It shows that combining various methods is essential for correct synchronization detection and characterizes the transition to almost synchronization in non-identical chaotic pendula.

Findings

Multiple methods are needed for accurate synchronization detection.

Almost synchronization occurs when Lyapunov exponents are nearly equal.

Transition to synchronization involves frequency entrainment unaffected by amplitude mismatch.

Abstract

Auxiliary system approach and various nearest neighbor methods are widely used to detect generalized synchronization in non-identical coupled systems. These methods generally give contradictory results. Therefore one method alone is not sufficient to predict correct result. We show in this report that it is necessary to apply multiple methods together to come to a conclusion. These methods show a signature of generalized synchronization in diffusively coupled non-identical chaotic parametric excited pendula. But we finally find it to be the almost synchronization. It is achieved when the second Lyapunov exponent and both the system's transverse Lyapunov exponents are almost equal. The transition from asynchronous state to almost synchronization is through frequency entrainment as coupling constant is increased. Non-identity of the pendula are realized by mismatch in amplitude of parametric forcing. The frequency entrainment regime does not depend on amplitude mismatch whereas onset of almost synchronization increases with increase in mismatch. The systems