Self-organized network of phase oscillators coupled by activity-dependent interactions

Area of Science:

• Complex Systems
• Nonlinear Dynamics
• Network Science

Background:

• Coupled oscillators are fundamental to understanding emergent collective behavior in various natural and engineered systems.
• The dynamics of interactions between oscillators often play a crucial role in shaping system-level patterns.
• Investigating adaptive interaction rules is key to uncovering novel self-organization mechanisms.

Purpose of the Study:

• To explore the collective behaviors emerging from a network of coupled phase oscillators with dynamically evolving interactions.
• To identify and characterize the distinct states of collective behavior in such coevolving systems.
• To demonstrate the potential for designing specific collective states, such as multiclusters, through controlled interaction dynamics.

Main Methods:

• Modeling a network of coupled phase oscillators with interaction weights that adapt based on relative oscillator phases.
• Analyzing the emergent states of collective behavior through numerical simulations and theoretical analysis.
• Investigating the influence of weight dynamics on the formation of synchronized, coherent, and chaotic states.

Main Results:

• The coevolving dynamical system robustly generates three fundamental collective states: two-cluster, coherent, and chaotic.
• Oscillator phase patterns and interaction network weights are simultaneously organized via coevolution.
• Self-assembled multicluster states can be achieved by precisely controlling the weight dynamics.

Conclusions:

• The study provides a framework for understanding how adaptive interactions drive self-organization in rhythmic systems.
• The findings offer insights into the design principles for engineering collective behavior in complex networks.
• This work advances the understanding of emergent phenomena in systems with coevolving dynamics.