Effect of adaptation functions and multilayer topology on synchronization

Area of Science:

• Complex systems
• Nonlinear dynamics
• Statistical physics

Background:

• Kuramoto oscillators are fundamental models for studying synchronization phenomena in coupled dynamical systems.
• Adaptive coupling, where interaction strength depends on system state, introduces complex dynamics not seen in fixed-coupling models.
• Multilayer networks offer a richer framework for understanding emergent behavior compared to single-layer systems.

Purpose of the Study:

• To analytically investigate the synchronization dynamics of globally coupled Kuramoto oscillators with adaptive pairwise interactions.
• To extend the adaptive coupling framework to multilayer configurations, specifically a bilayer model.
• To uncover novel transition scenarios in adaptive multilayer networks, particularly those with cross-adaptive interlayer interactions.

Main Methods:

• Analytical investigation using the Ott-Antonsen ansatz for adaptive coupling functions.
• Development of a theoretical formulation for adaptively coupled multilayer systems.
• Simulation and analysis of a bilayer model with cross-adaptive interlayer coupling.

Main Results:

• Identified two broad classes of adaptation functions governing the route to synchronization in monolayer systems.
• Demonstrated that adaptive multilayer configurations exhibit a wider range of synchronization behaviors than monolayer systems.
• Uncovered distinct transition scenarios in bilayer models due to cross-adaptive interlayer interactions.

Conclusions:

• Adaptive coupling significantly enriches the synchronization dynamics of Kuramoto oscillator networks.
• Multilayer adaptive networks provide a powerful platform for exploring complex emergent phenomena.
• The findings offer insights into the control and design of synchronized behavior in diverse complex systems.