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Published on: June 8, 2018
Multiphase patterns in periodically forced oscillatory systems
Summary
We discovered a novel instability in oscillatory systems under periodic forcing. Stationary patterns can decompose into traveling waves, transitioning from two-phase to multi-phase dynamics in 4:1 resonance.
Area of Science:
- Physics
- Nonlinear Dynamics
- Complex Systems
Background:
- Periodic forcing of oscillatory systems leads to frequency locking.
- Extended oscillatory systems exhibit complex behaviors, including multiple stable states.
Purpose of the Study:
- Investigate front solutions and their stability in extended oscillatory systems near a Hopf bifurcation.
- Analyze the 4:1 resonance where system frequency is 1/4 of forcing frequency.
- Explore transitions between stationary and traveling phase patterns.
Main Methods:
- Amplitude equation approach near a Hopf bifurcation.
- Analysis of front solutions (π fronts and π/2 fronts).
- Investigated front instability and degeneracy using cubic and quintic nonlinearities.
- Numerical simulations of spiral wave collapse.
Main Results:
- Identified a front instability where stationary π fronts decompose into traveling π/2 fronts.
- Found degeneracy in cubic nonlinearities, leading to a family of pair solutions.
- Quintic nonlinearities lift degeneracy but preserve instability nature.
- Demonstrated collapse of a four-phase spiral wave to a stationary two-phase pattern numerically.
Conclusions:
- Stationary π fronts can become unstable and decompose into traveling π/2 fronts.
- This instability signifies a transition from stationary two-phase to traveling multi-phase patterns.
- Similar instabilities are conjectured for higher 2n:1 resonances, indicating universal transition dynamics.
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