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Synchronous chaos in coupled map lattices with small-world interactions
Summary
Synchronous chaos is a stable attractor in systems with small-world couplings, where randomness enhances synchronization. System size influences collective behavior through size-dependent bifurcations.
Area of Science:
- Physics
- Complex Systems
- Network Science
Background:
- Extensive interactions are common in physical systems.
- Small-world networks exhibit unique topological properties.
Purpose of the Study:
- To investigate the role of small-world couplings in system dynamics.
- To determine the conditions for synchronous chaos.
- To analyze the impact of network structure on collective behavior.
Main Methods:
- Analysis of systems with a fixed fraction of nonlocal couplings.
- Examination in the thermodynamic limit.
- Study of size-dependent bifurcations.
Main Results:
- Synchronous chaos is a stable attractor for small-world couplings.
- Randomness in couplings promotes synchronization.
- Collective behavior exhibits size-dependent bifurcations.
Conclusions:
- Small-world networks facilitate stable synchronous chaos.
- Network randomness is crucial for synchronization.
- System size critically affects emergent collective behavior.