Multiphase patterns in periodically forced oscillatory systems
- Centro de Fisica No Lineal y Sistemas Complejos de Santiago, Casilla 17122, Santiago (Chile)
- Theoretical Division and Center for Nonlinear Studies, MSB284, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
- The Jacob Blaustein Institute for Desert Research and the Physics Department, Ben-Gurion University, Sede Boker Campus 84990 (Israel)
Periodic forcing of an oscillatory system produces frequency locking bands within which the system frequency is rationally related to the forcing frequency. We study extended oscillatory systems that respond to uniform periodic forcing at one quarter of the forcing frequency (the 4:1 resonance). These systems possess four coexisting stable states, corresponding to uniform oscillations with successive phase shifts of {pi}/2. Using an amplitude equation approach near a Hopf bifurcation to uniform oscillations, we study front solutions connecting different phase states. These solutions divide into two groups: {pi} fronts separating states with a phase shift of {pi} and {pi}/2 fronts separating states with a phase shift of {pi}/2. We find a type of front instability where a stationary {pi} front {open_quotes}decomposes{close_quotes} into a pair of traveling {pi}/2 fronts as the forcing strength is decreased. The instability is degenerate for an amplitude equation with cubic nonlinearities. At the instability point a continuous family of pair solutions exists, consisting of {pi}/2 fronts separated by distances ranging from zero to infinity. Quintic nonlinearities lift the degeneracy at the instability point but do not change the basic nature of the instability. We conjecture the existence of similar instabilities in higher 2n:1 resonances (n=3,4,{hor_ellipsis}) where stationary {pi} fronts decompose into {ital n} traveling {pi}/n fronts. The instabilities designate transitions from stationary two-phase patterns to traveling 2n-phase patterns. As an example, we demonstrate with a numerical solution the collapse of a four-phase spiral wave into a stationary two-phase pattern as the forcing strength within the 4:1 resonance is increased. {copyright} {ital 1999} {ital The American Physical Society}
- OSTI ID:
- 338689
- Journal Information:
- Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Vol. 59, Issue 5; Other Information: PBD: May 1999
- Country of Publication:
- United States
- Language:
- English
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