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State-dependent vulnerability of synchronization.
Everton S Medeiros1,2, Rene O Medrano-T3, Iberê L Caldas1
1Institute of Physics, University of São Paulo, Rua do Matão, Travessa R 187, 05508-090, São Paulo, Brazil.
Physical Review. E
|December 25, 2019
Summary
Complex networks exhibit state-dependent vulnerability in synchronization. Disturbances can either disrupt or restore synchronization based on the network
Area of Science:
- Complex networks
- Nonlinear dynamics
- Electronic circuit simulations
Background:
- Synchronization in complex networks is crucial for many systems.
- Understanding network vulnerability to perturbations is essential.
- Previous studies often assume state-independent responses.
Purpose of the Study:
- To investigate the state-dependent vulnerability of synchronization in complex networks.
- To analyze how perturbations affect synchronization outcomes at different network states.
- To identify the underlying mechanisms causing this vulnerability.
Main Methods:
- Numerically simulating complex networks of electronic circuits.
- Systematically applying perturbations to network units at various trajectory states.
- Quantifying synchronization changes and defining a safety index between states.
Main Results:
- Synchronization vulnerability is highly dependent on the network's current state.
- Perturbations can unpredictably either desynchronize or restore synchronization.
- A safety index reveals complex interactions between consecutive states.
Conclusions:
- The observed vulnerability stems from an unstable chaotic set within the system's state space.
- Network synchronization is not uniformly robust and exhibits state-specific fragility.
- This highlights the need for state-aware control strategies in complex networks.
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