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Transition to complete synchronization and global intermittent synchronization in an array of time-delay systems
R Suresh1, D V Senthilkumar, M Lakshmanan
1Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirapalli 620 024, India.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 26, 2012
Summary
We explored how time-delay systems transition to complete synchronization (CS). Different coupling methods lead to distinct synchronization patterns, including a novel global intermittent synchronization.
Area of Science:
- Nonlinear Dynamics
- Complex Systems
- Chaos Theory
Background:
- Time-delay systems exhibit complex behaviors, including synchronization.
- Understanding transitions to synchronization is crucial for analyzing coupled dynamical systems.
- Coupling configurations significantly influence synchronization dynamics.
Purpose of the Study:
- To investigate the nature of transitions from nonsynchronous states to complete synchronization (CS) in arrays of time-delay systems.
- To analyze how different coupling configurations (unidirectional and mutual) affect synchronization transitions.
- To characterize a newly observed synchronization phenomenon termed global intermittent synchronization.
Main Methods:
- Analysis of synchronization transitions in piecewise linear time-delay systems.
- Utilizing instantaneous diffusive coupling between system elements.
- Application of unstable periodic orbit theory to interpret synchronization transition phenomena.
Main Results:
- Synchronization transition dynamics differ significantly between unidirectional and mutual coupling.
- Unidirectional coupling shows distinct local and global synchronization transitions, with global occurring sequentially.
- Mutual coupling requires higher coupling strength for local synchronization, leading to immediate global synchronization.
- A novel 'global intermittent synchronization' characterized by synchronized bursts interrupting regular synchronization was observed.
Conclusions:
- The coupling configuration fundamentally dictates the pathway and characteristics of synchronization transitions in time-delay systems.
- Unstable periodic orbit theory provides a framework for understanding the observed synchronization transition types.
- The identified global intermittent synchronization represents a new phenomenon in coupled chaotic systems.
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