Concurrent enhancement of percolation and synchronization in adaptive networks

TL;DR

This paper demonstrates that adaptive networks of oscillators can self-organize from fragmented, incoherent states to connected, synchronized states with abrupt transitions, and that partial adaptation suffices for these enhancements.

Contribution

It introduces a stochastic, fitness-based adaptive rule for oscillator networks, showing concurrent enhancement of percolation and synchronization compared to non-adaptive networks.

Findings

Abrupt transitions to synchronization and percolation occur in adaptive networks.

Adaptive mechanisms significantly improve network connectivity and synchronization.

Partial adaptation is sufficient to achieve these collective behaviors.

Abstract

Co-evolutionary adaptive mechanisms are not only ubiquitous in nature, but also beneficial for the functioning of a variety of systems. We here consider an adaptive network of oscillators with a stochastic, fitness-based, rule of connectivity, and show that it self-organizes from fragmented and incoherent states to connected and synchronized ones. The synchronization and percolation are associated to abrupt transitions, and they are concurrently (and significantly) enhanced as compared to the non-adaptive case. Finally we provide evidence that only partial adaptation is sufficient to determine these enhancements. Our study, therefore, indicates that inclusion of simple adaptive mechanisms can efficiently describe some emergent features of networked systems' collective behaviors, and suggests also self-organized ways to control synchronization and percolation in natural and social systems.