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Invariance and stability conditions of interlayer synchronization manifold.
Sarbendu Rakshit1, Bidesh K Bera2,3, Dibakar Ghosh1
1Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108, India.
Physical Review. E
|February 20, 2020
Summary
This study explores interlayer synchronization in stochastic multiplex hypernetworks. We found conditions for synchronization invariance and stability, showing intralayer synchronization is impossible in this architecture.
Area of Science:
- Complex Networks
- Network Synchronization
- Statistical Physics
Background:
- Multiplex networks feature multiple layers of interactions.
- Hypernetworks represent higher-order interactions.
- Interlayer synchronization is crucial for understanding complex system dynamics.
Purpose of the Study:
- Investigate interlayer synchronization in stochastic multiplex hypernetworks.
- Determine conditions for the invariance and stability of interlayer synchronization.
- Analyze the possibility of intralayer synchronization in this network architecture.
Main Methods:
- Analytical derivation using the master stability function approach.
- Construction of a Lyapunov function for global stability analysis.
- Modeling stochasticity through rewiring probabilities in network connections.
Main Results:
- Derived necessary-sufficient conditions for local stability of interlayer synchronization.
- Established a sufficient condition for global stability.
- Proved that intralayer synchronization is unattainable due to stochastic interlayer connections.
- Invariance and stability conditions hold for all rewiring probabilities.
Conclusions:
- The study provides a comprehensive framework for understanding interlayer synchronization in stochastic multiplex hypernetworks.
- The derived conditions for invariance and stability are robust across various rewiring probabilities.
- The findings highlight limitations in achieving intralayer synchronization within this specific network architecture.
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