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Dynamics of phase slips in systems with time-periodic modulation
Punit Gandhi1, Edgar Knobloch1, Cédric Beaume2
1Department of Physics, University of California, Berkeley, California 94720, USA.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 15, 2016
Summary
Researchers studied the Adler equation with time-periodic frequency modulation, identifying resonances between modulation period and phase slip generation. This reveals complex parameter space structures with integer and noninteger phase slips, including canard trajectories.
Area of Science:
- Nonlinear dynamics
- Theoretical physics
- Mathematical modeling
Background:
- The Adler equation models systems with frequency modulation.
- Understanding resonances is crucial for predicting system behavior.
- Phase slips are key events in many physical phenomena.
Purpose of the Study:
- To investigate the Adler equation under time-periodic frequency modulation.
- To identify and characterize resonances between modulation and phase slip timescales.
- To map the parameter space structure and identify unique dynamical behaviors.
Main Methods:
- Numerical continuation for parameter space exploration.
- Time simulations to observe system evolution.
- Asymptotic methods for analytical insights, particularly in the low-frequency regime.
Main Results:
- Identified a series of resonances linked to phase slip generation.
- Characterized parameter space regions with integer and noninteger phase slips per modulation period.
- Observed canard trajectories drifting along unstable equilibria.
Conclusions:
- The study reveals intricate parameter space structures driven by frequency modulation.
- An adiabatic description accurately models the low-frequency modulation regime.
- Resonances play a critical role in the dynamics of phase slip generation.
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