Synchronization and Anti-synchroniztion of Dynamically Coupled Networks

TL;DR

This paper studies how two coupled networks of two-state nodes can synchronize or anti-synchronize, using Langevin equations and information theory, revealing conditions for optimal information transfer and discussing modeling limitations.

Contribution

It introduces a Langevin equation framework for coupled networks with partial interconnections, explaining synchronization phenomena and linking them to information transfer and criticality.

Findings

Synchronization depends on the sign of inter-network coupling.

Maximum information transfer occurs near the critical state.

Langevin models have limitations in representing network dynamics.

Abstract

We consider the coupling between two networks, each having N nodes whose individual dynamics is modeled by a two-state master equation. The intra-network interactions are all to all, whereas the inter-network interactions involve only a small percentage of the total number of nodes. We demonstrate that the dynamics of the mean field for a single network has an equivalent description in terms of a Langevin equation for a particle in a double-well potential. The coupling of two networks or equivalent coupling of two Langevin equations demonstrates synchronization or antisynchronization between two systems, depending on the sign of the interaction. The anti-synchronized behavior is explained in terms of the potential function and the inter-network interaction. The relative entropy is used to establish that the conditions for maximum information transfer between the networks are consistent with the Principle of Complexity Management and occurs when one system is near the critical state. The limitations of the Langevin modeling of the network coupling are also discussed.