Symmetrically space-shifted feedback control of nonlinear dissipative wavesY. Tonosaki1, H. Tokuda1, V. S. Zykov2 and T. Ohta1
1 Department of Physics, Kyoto University - Kyoto, 606-8502, Japan
2 Institut für Theoretische Physik, Technische Universität Berlin - Hardenbergstrasse 36, D-10623 Berlin, Germany, EU
received 13 March 2008; accepted in final form 15 July 2008; published September 2008
published online 3 September 2008
Dynamics of nonlinear dissipative waves propagating in one dimension under a feedback-mediated spatio-temporal forcing is investigated. The feedback induced in the time evolution equation is taken to be proportional to the sum of two spatial wave profiles shifted in the forward and backward directions at the same space shift . It is found that, when the magnitude of the feedback exceeds a certain critical value depending on , the waves cease propagating. This phenomenon can be understood almost completely by a phase dynamics approach.
05.45.-a - Nonlinear dynamics and chaos.
47.54.-r - Pattern selection; pattern formation.
82.40.Ck - Pattern formation in reactions with diffusion, flow and heat transfer.
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