Asymmetry-induced order in multilayer networks.

Area of Science:

• Complex systems
• Network science
• Theoretical ecology

Background:

• Network symmetries often enhance synchronization stability.
• Real-world networks exhibit inherent symmetries influencing dynamics.

Purpose of the Study:

• To investigate how breaking network symmetry affects system dynamics.
• To demonstrate the phenomenon of asymmetry-induced order.
• To analyze the underlying mechanisms and bifurcation scenarios.

Main Methods:

• Analysis of an ecological multilayer network with natural topological asymmetries.
• Analytical and numerical investigation of system dynamics on the synchronization manifold.
• Coupling paradigmatic Rössler and Lorenz systems to test generic node dynamics.

Main Results:

• Breaking interaction symmetry can induce macroscopic order, such as regularity.
• Asymmetries rescue systems from chaotic oscillations, establishing stable periodic orbits and equilibria.
• The mechanism involves the absence of dynamics on the synchronization manifold.
• A bifurcation scenario detailing the route from chaos to order was identified.

Conclusions:

• Asymmetry-induced order is a robust phenomenon applicable to various network types and node dynamics.
• This finding challenges the conventional view that symmetry is solely responsible for order in networks.
• The study provides a novel perspective on controlling chaos and achieving stability in complex systems.