Dresden 2003 – scientific programme

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DY: Dynamik und Statistische Physik

DY 40: Nonlinear dynamics III

DY 40.3: Talk

Thursday, March 27, 2003, 10:15–10:30, G\"OR/226

Periodic forcing and feedback control of nonlinear oscillators and meandering spiral waves — •V. Zykov, G. Bordiougov, H. Brandtstaedter, I. Gerdes, and H. Engel — Institut fuer Theoretische Physik, Technische Universitaet Berlin, Hardenbergstr. 36, D-10623 Berlin, Germany

It is shown that meandering spiral waves rotating in excitable media subjected to periodic external forcing or feedback control resemble many features of nonlinear lumped oscillators. In particular, the period shift function obtained for the Poincare oscillator is qualitatively identical to that determined for spiral waves under fixed phase control. On the other hand, three types of attractors (resonance, entrainment, and asynchronous) of meandering spiral waves are observed in experiments with the light-sensitive Belousov-Zhabotinsky reaction under one-channel feedback control and in numerical simulations performed for the underlying Oregonator model. These dynamic regimes appear as specific features of a distributed system. A theory of the resonance attractor for meandering spiral waves is developed which predicts the attractor radius and specifies the basins of attraction. The presented theoretical description is in good quantitative agreement with the performed numerical computations and the experimental observations.