Occasional uncoupling overcomes measure desynchronization

TL;DR

This paper investigates measure synchronization in Hamiltonian systems, revealing that occasional uncoupling can restore synchronization during desynchronized intervals, with analytical insights into optimal timing for periodic uncoupling.

Contribution

It introduces the concept that intermittent uncoupling can recover measure synchronization in Hamiltonian systems, providing analytical conditions for effective timing.

Findings

Occasional uncoupling restores measure synchronization in Hamiltonian systems.

Desynchronized states can be re-synchronized through strategic intermittent uncoupling.

Analytical expressions for optimal uncoupling timing are derived.

Abstract

Owing to the absence of the phase space attractors in the Hamiltonian dynamical systems, the concept of the identical synchronization between the dissipative systems is inapplicable to the Hamiltonian systems for which, thus, one defines a related generalized phenomenon known as the measure synchronization. A coupled pair of Hamiltonian systems---the full coupled system also being Hamiltonian---can possibly be in two types of measure synchronized states: quasiperiodic and chaotic. In this paper, we take representative systems belonging to each such class of the coupled systems and highlight that, as the coupling strengths are varied, there may exist intervals in the ranges of the coupling parameters at which the systems are measure desynchronized. Subsequently, we illustrate that as a coupled system evolves in time, occasionally switching off the coupling when the system is in the measure desynchronized state can bring the system back in measure synchrony. Further, for the case of the occasional uncoupling being employed periodically and the corresponding time-period being small, we analytically find the values of the on-fraction of the time-period using which measure synchronization is effected on the corresponding desynchronized state.