Complexity and irreducibility of dynamics on networks of networks

TL;DR

This study explores how coupling multiple FitzHugh-Nagumo oscillator networks creates complex, rich dynamics and transitions, revealing that simplifying such systems to a single network may overlook critical behaviors.

Contribution

It demonstrates that networks of networks can exhibit more complex dynamics than single networks, highlighting the importance of considering the layered structure in understanding system behavior.

Findings

Identification of a parameter region with enhanced dynamical richness

Transitions to multistability near certain coupling regimes

Reduction of network complexity may miss key dynamical features

Abstract

We study numerically the dynamics of a network of all-to-all-coupled, identical sub-networks consisting of diffusively coupled, non-identical FitzHugh--Nagumo oscillators. For a large range of within- and between-network couplings, the network exhibits a variety of dynamical behaviors, previously described for single, uncoupled networks. We identify a region in parameter space in which the interplay of within- and between-network couplings allows for a richer dynamical behavior than can be observed for a single sub-network. Adjoining this atypical region, our network of networks exhibits transitions to multistability. We elucidate bifurcations governing the transitions between the various dynamics when crossing this region and discuss how varying the couplings affects the effective structure of our network of networks. Our findings indicate that reducing a network of networks to a single (but bigger) network might be not accurate enough to properly understand the complexity of its dynamics.