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Antiphase synchronization in multiplex networks with attractive and repulsive interactions.
Sayantan Nag Chowdhury1, Sarbendu Rakshit1, Javier M Buldú2,3,4
1Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata-700108, India.
Physical Review. E
|April 17, 2021
Summary
This study explores synchronization in multilayer networks with mixed attractive and repulsive interactions. Researchers found a transition from antisynchronization to antiphase synchrony in complex network systems.
Area of Science:
- Network Science
- Complex Systems
- Dynamical Systems
Background:
- Recent research explores mixed attractive and repulsive interactions in single-layer networks, drawing parallels with spin glasses, neural networks, and ecological systems.
- Existing studies are limited to single-layer networks, necessitating analysis of multilayer configurations for complex dynamics and equilibrium states.
Purpose of the Study:
- Investigate synchronization properties in multilayer dynamical systems with attractive intralayer and repulsive interlayer connections.
- Analyze the emergence of antisynchronization (intralayer synchronization with antiphase dynamics between layers).
- Examine the transition from antisynchronization to antiphase synchrony in bipartite multiplex architectures.
Main Methods:
- Analytical identification of graph topologies for interlayer antisynchronization.
- Derivation of intralayer synchronization manifold invariance and attractor size calculation.
- Application of the master stability function approach for local stability analysis.
Main Results:
- Demonstrated a transition from interlayer antisynchronization to antiphase synchrony in connected bipartite multiplex architectures when repulsive coupling is introduced via a spanning tree.
- Identified analytical conditions for interlayer antisynchronization, its interplay with intralayer and antiphase synchronization.
- Provided and numerically validated necessary conditions for coexisting interlayer antisynchronization and intralayer synchronization using Stuart-Landau oscillators.
Conclusions:
- The study elucidates the synchronization dynamics in multilayer networks with competing interactions.
- Analytical and numerical findings offer insights into the conditions governing antisynchronization and antiphase synchrony.
- The master stability function approach confirms the stability of the interlayer antisynchronization state.
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