Understanding transient uncoupling induced synchronization through modified dynamic coupling

TL;DR

This paper investigates how transient uncoupling induces synchronization in chaotic systems at high coupling strengths, revealing the underlying dynamics and proposing a modified coupling scheme for improved synchronization control.

Contribution

It introduces a novel understanding of transient decay phenomena and develops a modified dynamic coupling scheme to explain and enhance synchronization in chaotic systems.

Findings

Optimal coupling regions are characterized by eigenvalue conditions.

Transient decay can occur even when trajectories diverge asymptotically.

Modified coupling scheme outperforms traditional dynamic coupling.

Abstract

An important aspect of the recently introduced transient uncoupling scheme is that it induces synchronization for large values of coupling strength at which the coupled chaotic systems resist synchronization when continu- ously coupled. However, why this is so is an open problem. To answer this question, we recall the conventional wisdom that the eigenvalues of the Jacobian of the transverse dynamics measure whether a trajectory at a phase point is locally contracting or diverging with respect to another nearby trajectory. Subsequently, we go on to highlight a lesser appreciated fact that even when, under the corresponding linearised flow, the nearby trajectory asymptotically diverges away, its distance from the reference trajectory may still be contracting for some intermediate period. We term this phenomenon transient decay in line with the phenomenon of the transient growth. Using these facts, we show that an optimal coupling region, i.e., a region of the phase space where coupling is on, should ideally be such that at any of the constituent phase point either the maximum of the real parts of the eigenvalues is negative or the magnitude of the positive maximum is lesser than that of the negative minimum. We also invent and employ modified dynamics coupling scheme---a significant improvement over the well-known dynamic coupling scheme---as a decisive tool to justify our results.