Experimental confirmation of chaotic phase synchronization in coupled time-delayed electronic circuits
D V Senthilkumar1, K Srinivasan, K Murali
1Centre for Dynamics of Complex Systems, University of Potsdam, Potsdam, Germany.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 15, 2011
Summary
We experimentally demonstrated chaotic phase synchronization (CPS) in coupled time-delay systems using electronic circuits. A new method, localized sets, effectively characterizes this complex phenomenon.
Area of Science:
- Nonlinear Dynamics
- Chaos Theory
- Experimental Physics
Background:
- Coupled nonlinear systems exhibit complex behaviors.
- Time-delay systems are crucial in various scientific and engineering fields.
- Chaotic Phase Synchronization (CPS) is a complex synchronization mode in chaotic systems.
Purpose of the Study:
- To experimentally demonstrate chaotic phase synchronization (CPS) in unidirectionally coupled time-delay systems.
- To implement and validate an efficient method for characterizing CPS using localized sets.
- To corroborate experimental findings with numerical simulations.
Main Methods:
- Utilized electronic circuits to create unidirectionally coupled time-delay systems.
- Implemented the localized sets methodology for CPS characterization.
- Performed numerical simulations including phase differences, localized sets, Lyapunov exponents, and correlation of probability of recurrence (C(CPR)).
Main Results:
- Successfully demonstrated chaotic phase synchronization (CPS) experimentally.
- Localized sets were confirmed as an effective tool for characterizing CPS.
- Experimental observations were consistent with numerical results from multiple analytical approaches.
Conclusions:
- The experimental demonstration validates CPS in coupled time-delay systems.
- Localized sets provide a robust method for identifying and characterizing CPS.
- The study bridges experimental and numerical findings in chaotic synchronization.
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