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Transition from anticipatory to lag synchronization via complete synchronization in time-delay systems
D V Senthilkumar1, M Lakshmanan
1Centre for Nonlinear Dynamics, Department of Physics, Bharathidasan University, Tiruchirapalli 620 024, India. skumar@cnld.bdu.ac.in
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 9, 2005
Summary
This study identifies anticipatory, complete, and lag synchronization in systems with feedback and coupling delays. Stability conditions are independent of delay times, enabling all three synchronization types and transitions between them.
Area of Science:
- Nonlinear Dynamics
- Chaos Theory
- Complex Systems
Background:
- Time delays are crucial in many dynamical systems.
- Understanding synchronization phenomena in systems with delays is essential.
Purpose of the Study:
- To investigate anticipatory, complete, and lag synchronization in a system with two distinct time delays.
- To analyze the transitions between these synchronization types based on coupling delay.
- To characterize the emergence of synchronization from a desynchronized state.
Main Methods:
- Analysis of a single system with feedback delay (tau1) and coupling delay (tau2).
- Investigation of stability conditions for different synchronization regimes.
- Characterization of synchronization transitions using a similarity function and analysis of laminar phase distribution.
Main Results:
- Identified anticipatory, complete, and lag synchronization.
- Demonstrated that stability conditions are independent of delay times (tau1, tau2).
- Showcased transitions between synchronization types by varying coupling delay (tau2) and system parameter (b2).
- Observed emergence of exact synchronization via approximate synchronization and on-off intermittency.
Conclusions:
- All three synchronization types (anticipatory, complete, lag) are achievable by tuning system parameters and delays.
- The stability of synchronization is robust to variations in delay times.
- System parameter variations drive transitions from desynchronized states through approximate synchronization to various exact synchronization forms.