Dynamic link switching induces stable synchronized states in sparse networks

TL;DR

This paper demonstrates that dynamically switching links in sparse double-layer networks of FitzHugh-Nagumo oscillators can induce stable inter-layer synchronization, even when individual layers are chaotic, by analyzing switching effects and stability regions.

Contribution

It introduces a novel approach of link switching to promote synchronization in sparse, chaotic networks, supported by MSF analysis and numerical simulations.

Findings

Switching links induces inter-layer synchronization.

Shorter switching times enhance synchronization.

Chaos persists despite synchronization, confirmed by Lyapunov exponents.

Abstract

The flow of information in networked systems composed of multiple interacting elements strongly depends on the level of connectivity among these elements. Sparse connectivity often hinders the emergence of states in which information is globally shared, such as fully synchronized states. In this context, dynamically switching existing network links among system elements can facilitate the onset of synchronization. Here, we address this problem in a double-layer network of FitzHugh-Nagumo oscillators with sparse inter-layer connectivity at fixed density. We show that dynamically switching the existing cross-layer links induces inter-layer synchronization, with a clear dependence on the switching time. In agreement with intuition, shorter switching times suppress large deviations between temporally connected oscillators and more effectively promote synchronization; crucially, this effect persists even when each isolated layer is chaotic. Chaos at the layer level is verified by a strictly positive largest Lyapunov exponent, confirming that synchrony is induced by switching rather than by periodic dynamics. For a minimal double-layer system, we emulate switching using smooth square waves and compute the master stability function (MSF), which is in agreement with direct numerical simulations and delineates the stability regions in parameter space.