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Collective dynamics of multiplex networks with distinct adaptation rules
Akash Yadav1, Qazi Saaheelur Rahaman1,2, V K Chandrasekar3
1Indian Institute of Science Education and Research, School of Physics, Thiruvananthapuram 695551, Kerala, India.
Physical Review. E
|January 21, 2026
Summary
We explored collective dynamics in multiplex networks of adaptively coupled Kuramoto oscillators. Different adaptation rules create rich collective states not seen in single-layer networks.
Area of Science:
- Complex Systems
- Network Science
- Nonlinear Dynamics
Background:
- Multiplex networks consist of multiple layers of interconnected nodes.
- Adaptive coupling allows network structure to change over time.
- Kuramoto oscillators are a standard model for studying synchronization phenomena.
Purpose of the Study:
- To investigate the collective dynamics of multiplex networks with layer-specific adaptive rules.
- To identify and characterize emergent collective states.
- To understand the role of interlayer coupling in synchronization.
Main Methods:
- Simulations of adaptively coupled Kuramoto oscillators on multiplex networks.
- Characterization of collective states using intralayer and interlayer order parameters.
- Analytical estimation of critical coupling strength using the collective coordinate approach.
Main Results:
- Discovery of diverse collective states: incoherent, antipodal-incoherent, antipodal cluster, antipodal-partially coherent, mixed, and antipodal states.
- Demonstration that multiplexing and distinct adaptation rules lead to novel collective behaviors.
- Validation of analytical predictions for interlayer frequency synchronization.
Conclusions:
- The interplay of adaptation mechanisms in multiplex networks generates complex collective dynamics.
- Multiplexity is crucial for observing states beyond those in single-layer systems.
- Analytical methods can accurately predict synchronization thresholds in these complex systems.
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