Sparsity-driven synchronization in oscillators networks

TL;DR

This paper introduces a novel phenomenon where removing links in sparse oscillator networks induces complete synchronization, supported by numerical, analytical, and bifurcation analysis, with potential control applications.

Contribution

It reveals sparsity-driven synchronization, showing how link removal in sparse networks guarantees complete synchronization, a novel control mechanism for complex systems.

Findings

Complete synchronization achieved by link removal in sparse networks

Analytical bifurcation analysis explains the transition to synchronization

Procedure to determine minimal link removal for synchronization

Abstract

The emergence of synchronized behavior is a direct consequence of networking dynamical systems. Naturally, strict instances of this phenomenon, such as the states of complete synchronization are favored, or even ensured, in networks with a high density of connections. Conversely, in sparse networks, the system state-space is often shared by a variety of coexistent solutions. Consequently, the convergence to complete synchronized states is far from being certain. In this scenario, we report the surprising phenomenon in which completely synchronized states are made the sole attractor of sparse networks by removing network links, the sparsity-driven synchronization. This phenomenon is observed numerically for nonlocally coupled Kuramoto networks and verified analytically for locally coupled ones. In addition, we reduce the network equations to a one-dimension dynamical system to unravel the bifurcation scenario underlying the network transition to completely synchronized behavior. Furthermore, we present a simple procedure, based on the bifurcations in the thermodynamic limit, that determines the minimum number of links to be removed in order to ensure complete synchronization. Finally, we propose an application of the reported phenomenon as a control scheme to drive complete synchronization in high connectivity networks.