Four-phase patterns in forced oscillatory systems
- Center for Nonlinear Dynamics and Department of Physics, The University of Texas at Austin, Austin, Texas 78712 (United States)
- Center for Nonlinear Studies and T-7, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
- CFD Laboratory and ASE/ME Department, The University of Texas at Austin, Austin, Texas 78712 (United States)
- Department of Energy and Environmental Physics, BIDR, and Physics Department, Ben-Gurion University, Sede Boker Campus 84990, (Israel)
We investigate pattern formation in self-oscillating systems forced by an external periodic perturbation. Experimental observations and numerical studies of reaction-diffusion systems and an analysis of an amplitude equation are presented. The oscillations in each of these systems entrain to rational multiples of the perturbation frequency for certain values of the forcing frequency and amplitude. We focus on the subharmonic resonant case where the system locks at one-fourth the driving frequency, and four-phase rotating spiral patterns are observed at low forcing amplitudes. The spiral patterns are studied using an amplitude equation for periodically forced oscillating systems. The analysis predicts a bifurcation (with increasing forcing) from rotating four-phase spirals to standing two-phase patterns. This bifurcation is also found in periodically forced reaction-diffusion equations, the FitzHugh-Nagumo and Brusselator models, even far from the onset of oscillations where the amplitude equation analysis is not strictly valid. In a Belousov-Zhabotinsky chemical system periodically forced with light we also observe four-phase rotating spiral wave patterns. However, we have not observed the transition to standing two-phase patterns, possibly because with increasing light intensity the reaction kinetics become excitable rather than oscillatory. (c) 2000 The American Physical Society.
- OSTI ID:
- 20217621
- Journal Information:
- Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Vol. 62, Issue 3; Other Information: PBD: Sep 2000; ISSN 1063-651X
- Country of Publication:
- United States
- Language:
- English
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