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Mathematical Biology seminar
Arik Yochelis
Department of Chemical Engineering,
Technion - Israel Institute of Technology
"Synchronous entrainment (frequency locking) in spatially extended
forced oscillations: From chemical oscillations to universality"
Thursday July 15, 2004
3:05 pm LCB 215
An oscillator subjected to external periodic forcing may exhibit entrained,
quasi-periodic or chaotic dynamical motions. Entrainment or frequency
locking phenomena can be observed in auto-oscillatory systems either
by local coupling or by externally applied periodic forcing; examples
include nonlinear optics, chemical reactions or biological rhythms. A
system is frequency locked when its oscillation frequency is adjusted
to an irreducible fraction of the forcing frequency. Although the
frequency locking phenomena have been extensively studied for single
oscillator type systems, the fundamental description of resonance
phenomena for spatially extended systems is missing.
Our research is concerned with frequency locking phenomena in
spatially extended media and addresses the effects of pattern
formation on resonance behavior. The study has been motivated by
recent experiments on temporally driven Belousov-Zhabotinsky
reaction-diffusion systems focusing on standing-wave patterns. We
study pattern formation mechanisms and parameters ranges where
resonant and non-resonant standing-wave patterns are developed. The
analysis is based on the complex forced Ginzburg-Landau equation which
describes universal dynamical behavior of periodically driven
oscillatory media. Amoung our results we show that in extended systems
spatial structures and instabilities may reduce or extend the
boundaries of frequency locking so that the resonance ranges for a
single oscillator do not always coincide with resonance ranges in
extended systems. At the end, we justify our results by confronting
experimental observations and extend the universal theoretical concept
of frequency locking to spatially extended systems.
For more information contact J. Keener, 1-6089
E-mail:
keener@math.utah.edu
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