Network synchronization with periodic coupling

TL;DR

This paper investigates how periodic coupling influences the synchronization of chaotic oscillators in networks, revealing that tuning the coupling frequency can significantly enhance or diminish network synchronizability.

Contribution

It provides a detailed analysis of the effect of coupling frequency on network synchronization using master stability function and finite-time Lyapunov exponents, highlighting characteristic frequencies for optimal synchronizability.

Findings

Network synchronizability peaks at specific characteristic frequencies.

Increasing coupling amplitude lowers these characteristic frequencies.

Finite-time Lyapunov exponent spectra indicate a transition from localized to broad distributions at optimal frequencies.

Abstract

The synchronization behavior of networked chaotic oscillators with periodic coupling is investigated. It is observed in simulations that the network synchronizability could be significantly influenced by tuning the coupling frequency, even making the network alternated between the synchronous and non-synchronous states. By the method of master stability function, we conduct a detailed analysis on the influence of coupling frequency on network synchronizability, and find that the network synchronizability is maximized at some characteristic frequencies comparable to the intrinsic frequency of the local dynamics. Moremore, it is found that as the amplitude of the coupling increases, the characteristic frequencies are gradually decreased. By the technique of finite-time Lyapunov exponent, we investigate further the mechanism for the maximized synchronizability, and find that at the characteristic frequencies the power spectrum of the finite-time Lyapunov exponent is abruptly changed from the localized to broad distributions. When this feature is absent or not prominent, the network synchronizability is less influenced by the periodic coupling. Our study shows the efficiency of finite-time Lyapunov exponent in exploring the synchronization behavior of temporally coupled oscillators, and sheds lights on the interplay between the system dynamics and structure in the general temporal networks.