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Phase locking of two limit cycle oscillators with delay coupling
1Saratov State University, 83 Astrakhanskaya st., Saratov 410012, Russia.
Chaos (Woodbury, N.Y.)
|July 3, 2014
Summary
Mutual phase locking between two coupled oscillators was studied. Synchronization modes, like in-phase and anti-phase, depend on signal phase shift, with more modes appearing as delay time increases.
Area of Science:
- Nonlinear dynamics
- Oscillator systems
- Synchronization phenomena
Background:
- Limit cycle oscillators are fundamental in modeling periodic phenomena.
- Coupling and delay are crucial factors influencing oscillator behavior.
- Mutual phase locking describes synchronized oscillations between systems.
Purpose of the Study:
- To investigate mutual phase locking in two delay-coupled limit cycle oscillators.
- To derive conditions for phase locking using a generalized Adler equation.
- To explore the impact of coupling phase shift and delay time on synchronization modes.
Main Methods:
- Analysis of a generalized Adler equation for phase locking conditions.
- Numerical simulations to validate analytical results.
- Systematic variation of coupling phase shift and delay time.
Main Results:
- Conditions for mutual phase locking were analytically derived.
- Synchronization can manifest as in-phase or anti-phase modes.
- Increased delay time leads to a higher number of possible synchronization modes.
Conclusions:
- The study provides a theoretical framework for understanding synchronization in delay-coupled oscillators.
- Phase shift and delay time are key parameters determining synchronization patterns.
- The findings are relevant for systems exhibiting coupled oscillatory behavior with time delays.
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