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Synchronization of chaotic oscillators due to common delay time modulation
Won-Ho Kye1, Muhan Choi, M S Kurdoglyan
1National Creative Research Initiative Center for Controlling Optical Chaos, Pai-Chai University, Daejeon 302-735, Korea.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 17, 2004
Summary
Two identical chaotic systems can synchronize when their delay times are modulated by a shared irregular signal. This synchronization phenomenon is analyzed using Lyapunov exponents.
Area of Science:
- Nonlinear Dynamics
- Chaos Theory
- Complex Systems
Background:
- Chaotic systems often exhibit complex, unpredictable behavior.
- Synchronization in chaotic systems is a well-studied phenomenon, typically requiring specific coupling conditions.
- Modulating delay times in chaotic systems can introduce novel dynamics.
Purpose of the Study:
- To investigate synchronization behavior in identical chaotic systems with modulated delay times.
- To explore the influence of a common irregular signal on the synchronization of chaotic systems.
- To analyze the relationship between delay time modulation and generalized synchronization.
Main Methods:
- Utilizing two identical chaotic maps and two identical chaotic oscillators.
- Modulating the delay times of these systems with a common chaotic or random signal.
- Analyzing the synchronization phenomenon using Lyapunov exponents.
Main Results:
- Demonstrated synchronization behavior between two identical chaotic systems under modulated delay times.
- Confirmed that a common irregular signal can drive synchronization.
- Observed this phenomenon in both chaotic maps and chaotic oscillators.
Conclusions:
- Common irregular signal modulation of delay times is a viable mechanism for inducing synchronization in identical chaotic systems.
- The findings contribute to the understanding of synchronization in complex dynamical systems.
- The phenomenon is related to generalized synchronization, offering avenues for further research.