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Random delays and the synchronization of chaotic maps
1Instituto de Física, Facultad de Ciencias, Universidad de la República, Montevideo, Uruguay.
Physical Review Letters
|May 21, 2005
Summary
We found that arrays of chaotic logistic maps can synchronize despite random delays. Synchronization occurs when coupling is strong enough, suppressing individual map chaos and forming a steady state.
Area of Science:
- Complex Systems
- Nonlinear Dynamics
- Chaos Theory
Background:
- Coupled chaotic systems often exhibit synchronization phenomena.
- Introducing random delays can disrupt synchronization in dynamical networks.
- Understanding synchronization in delayed networks is crucial for various applications.
Purpose of the Study:
- To investigate the synchronization dynamics of chaotic logistic maps with random delay times.
- To determine the conditions under which synchronization can be achieved in such systems.
- To analyze the impact of network topology and coupling strength on synchronization.
Main Methods:
- Numerical simulations of coupled chaotic logistic maps with random delays.
- Analysis of the synchronized state, identifying it as a homogeneous steady state.
- Statistical linear stability analysis to confirm numerical findings and understand delay effects.
Main Results:
- Synchronization is achieved for sufficient coupling strength, even with random delays.
- The synchronized state suppresses the chaotic dynamics of individual maps.
- Synchronization is independent of connection topology, depending primarily on the average number of links per node.
Conclusions:
- Coupled chaotic maps can synchronize robustly in the presence of random delays.
- The average connectivity, not the topology, is the key factor for synchronization.
- Random delayed interactions play a complex but crucial role in network synchronization.