Chaotic, informational and synchronous behaviour of multiplex networks

TL;DR

This paper explores how the topology of multiplex networks influences complex behaviors like chaos, information flow, and synchronization, providing analytical formulas and numerical studies on neural networks.

Contribution

It offers analytical formulas linking topology to behavior in multiplex networks with constant Jacobian and examines neural network behavior considering synapse types.

Findings

Behavior depends on Laplacian eigenvalues spectra in analytically tractable networks.

Symmetry breaking in topology affects network dynamics.

Chemical synapses disrupt the spectral-behavior relationship in neural networks.

Abstract

The understanding of the relationship between topology and behaviour in interconnected networks would allow to characterise and predict behaviour in many real complex networks since both are usually not simultaneously known. Most previous studies have focused on the relationship between topology and synchronisation. In this work, we provide analytical formulas that shows how topology drives complex behaviour: chaos, information, and weak or strong synchronisation; in multiplex networks with constant Jacobian. We also study this relationship numerically in multiplex networks of Hindmarsh-Rose neurons. Whereas behaviour in the analytically tractable network is a direct but not trivial consequence of the spectra of eigenvalues of the Laplacian matrix, where behaviour may strongly depend on the break of symmetry in the topology of interconnections, in Hindmarsh-Rose neural networks the nonlinear nature of the chemical synapses breaks the elegant mathematical connection between the spectra of eigenvalues of the Laplacian matrix and the behaviour of the network, creating networks whose behaviour strongly depends on the nature (chemical or electrical) of the inter synapses.