The Efficiency of Synchronization Dynamics and the Role of Network Syncreactivity

TL;DR

This paper introduces the concept of network syncreactivity and a transverse reactivity metric to improve synchronization strategies in coupled oscillator networks, demonstrating enhanced efficiency and robustness through dynamic coupling adjustments.

Contribution

It presents a novel metric called transverse reactivity for analyzing transient synchronization behavior and proposes a dynamic coupling strategy that outperforms traditional methods.

Findings

Dynamic coupling based on transverse reactivity achieves broader synchronization range.

Network syncreactivity correlates with transient synchronization efficiency.

Experimental validation confirms the effectiveness of the proposed strategy.

Abstract

Synchronization of coupled oscillators is a fundamental process in both natural and artificial networks. While much work has investigated the asymptotic stability of the synchronous solution, the fundamental question of the transient behavior toward synchronization has received far less attention. In this work, we present the transverse reactivity as a metric to quantify the instantaneous rate of growth or decay of desynchronizing perturbations. We first use the transverse reactivity to design a coupling-efficient and energy-efficient synchronization strategy that involves varying the coupling strength dynamically according to the current state of the system. We find that our synchronization strategy is able to synchronize networks in both simulation and experiment over a significantly larger (often by orders of magnitude) range of coupling strengths than is possible when the coupling strength is constant. Then, we characterize the effects of network topology on the transient dynamics towards synchronization by introducing the concept of network syncreactivity: A network with a larger syncreactivity has a larger transverse reactivity at every point on the synchronization manifold, independent of the oscillator dynamics. We classify real-world examples of complex networks in terms of their syncreactivity.