Effects of periodically modulated coupling on amplitude death in nonidentical oscillators

TL;DR

This paper investigates how periodic modulation of coupling strength affects amplitude death in nonidentical oscillators, revealing optimal modulation parameters and mechanisms for controlling oscillatory behavior.

Contribution

It introduces the impact of periodic coupling modulation on amplitude death, identifying optimal modulation parameters and analyzing the stability mechanism via Lyapunov exponents.

Findings

Optimal modulation amplitude maximizes AD domain.

Decreasing modulation frequency enlarges AD domain at small amplitudes.

Conditional Lyapunov exponent characterizes AD stability.

Abstract

The effects of periodically modulated coupling on amplitude death in two coupled nonidentical oscillators are explored. The AD domain could be significantly influenced by tuning the modulation amplitude and the modulation frequency of the modulated coupling strength. There is an optimal value of modulation amplitude for the modulated coupling with which the largest AD domain is observed in the parameter space. The AD domain is enlarged with the decrease of the modulation frequency for a given small modulation amplitude, while is shrunk with decrease of the modulation frequency for a given large modulation amplitude. The mechanism of AD in the presence of periodic modulation in the coupling is investigated via the local condition Lyapunov exponent of the coupled system. The stability of AD state can be well characterized by conditional Lyapunov exponent. The coupled system experiencing from the oscillatory state to AD is clearly indicated by the observation that the conditional Lyapunov exponent transits from positive to negative. Our results are helpful to many potential applications for the research of neuroscience and dynamical control in engineering.