Synchronization within synchronization: transients and intermittency in ecological networks

TL;DR

This paper reveals transient synchronization phenomena in ecological networks with chaotic predator-prey dynamics, showing how symmetry leads to temporary complete synchronization patterns that intermittently switch due to instability or noise.

Contribution

It introduces the concept of 'synchronization within synchronization' and provides a symmetry-based stability analysis for transient and intermittent synchronization behaviors in ecological networks.

Findings

Transient synchronization patterns follow algebraic scaling laws.

Complete synchronization occurs in symmetric pairs of patches.

Intermittent switching among synchronization patterns is driven by instability and noise.

Abstract

Transients are fundamental to ecological systems with significant implications to management, conservation, and biological control. We uncover a type of transient synchronization behavior in spatial ecological networks whose local dynamics are of the chaotic, predator-prey type. In the parameter regime where there is phase synchronization among all the patches, complete synchronization (i.e., synchronization in both phase and amplitude) can arise in certain pairs of patches as determined by the network symmetry - henceforth the phenomenon of "synchronization within synchronization." Distinct patterns of complete synchronization coexist but, due to intrinsic instability or noise, each pattern is a transient and there is random, intermittent switching among the patterns in the course of time evolution. The probability distribution of the transient time is found to follow an algebraic scaling law with a divergent average transient lifetime. Based on symmetry considerations, we develop a stability analysis to understand these phenomena. The general principle of symmetry can also be exploited to explain previously discovered, counterintuitive synchronization behaviors in ecological networks.