Dangerous Aging Transition in a Network of Coupled Oscillators

TL;DR

This paper studies a unique and dangerous aging transition in a network of coupled Van der Pol oscillators, revealing a sudden, abnormal phase transition driven by boundary crisis, differing from typical sinusoidal oscillator behavior.

Contribution

It identifies and analyzes a novel dangerous aging transition in Van der Pol oscillator networks, highlighting a different mechanism from traditional sinusoidal oscillators.

Findings

Discovered abnormal phase transition due to boundary crisis.

Demonstrated difference from sinusoidal oscillator transitions.

Provided bifurcation analysis of the transition mechanism.

Abstract

In this article, we investigate the dynamical robustness in a network of relaxation oscillators. In particular, we consider a network of diffusively coupled Van der Pol oscillators to explore the aging transition phenomena. Our investigation reveals that the mechanism of aging transition in a network of Van der Pol oscillator is quite different from that of typical sinusoidal oscillators such as Stuart-Landau oscillators. Unlike sinusoidal oscillators, the order parameter does not follow the second-order phase transition. Rather we observe an abnormal phase transition of the order parameter due to sudden unbounded trajectories at a critical point. We call it a dangerous aging transition. We provide details bifurcation analysis of such abnormal phase transition. We show that the boundary crisis of a limit-cycle oscillator is at the helm of such a dangerous aging transition.