Interlayer Hebbian Plasticity Induces First-Order Transition in Multiplex Networks

TL;DR

This paper demonstrates that Hebbian learning-based interlayer adaptation in multiplex networks causes an irreversible first-order transition to synchronization, with theoretical predictions confirmed by numerical simulations.

Contribution

It introduces a novel adaptive inter-layer process governed by Hebbian plasticity that induces a first-order synchronization transition in multiplex networks.

Findings

Adaptive Hebbian inter-layer coupling causes hysteresis in synchronization transitions.

Analytic predictions accurately determine critical coupling strengths.

Numerical simulations confirm the theoretical analysis of the transition behavior.

Abstract

Adaptation plays a pivotal role in the evolution of natural and artificial complex systems, and in the determination of their functionality. Here, we investigate the impact of adaptive inter-layer processes on intra-layer synchronization in multiplex networks. The considered adaptation mechanism is governed by a Hebbian learning rule, i.e., the link weight between a pair of interconnected nodes is enhanced if the two nodes are in phase. Such adaptive coupling induces an irreversible first-order transition route to synchronization accompanied with a hysteresis. We provide rigorous analytic predictions of the critical coupling strengths for the onset of synchronization and de-synchronization, and verify all our theoretical predictions by means of extensive numerical simulations.