Asymmetry-induced order in multilayer networks

TL;DR

This paper reveals that breaking symmetries in multilayer networks can induce order, transforming chaotic dynamics into stable states, with implications for understanding natural and engineered complex systems.

Contribution

It introduces the concept of asymmetry-induced order in multilayer networks and demonstrates its mechanism through analytical and numerical analysis, including generic node dynamics.

Findings

Asymmetries can stabilize periodic orbits and equilibria.

Symmetry breaking suppresses chaos in multilayer networks.

The phenomenon applies to various node dynamics like R"ossler and Lorenz systems.

Abstract

Symmetries naturally occur in real-world networks and can significantly influence the observed dynamics. For instance, many synchronization patterns result from the underlying network symmetries, and high symmetries are known to increase the stability of synchronization. Yet, here we find that general macroscopic features of network solutions such as regularity can be induced by breaking their symmetry of interactions. We demonstrate this effect in an ecological multilayer network where the topological asymmetries occur naturally. These asymmetries rescue the system from chaotic oscillations by establishing stable periodic orbits and equilibria. We call this phenomenon asymmetry-induced order and uncover its mechanism by analyzing both analytically and numerically the suppression of dynamics on the system's synchronization manifold. Moreover, the bifurcation scenario describing the route from chaos to order is also disclosed. We demonstrate that this result also holds for generic node dynamics by analyzing coupled paradigmatic R\"ossler and Lorenz systems.