Asymmetry-induced order in multilayer networks

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 Rössler and Lorenz systems.

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• Multiplexing-based control of wavefront propagation: the interplay of inter-layer coupling, asymmetry and noise
• Frequency Synchronization Induced by Frequency Detuning
• Coupling-induced periodic windows in networked discrete-time systems
• Disorder-promoted stability