Periodic forcing and feedback control of nonlinear lumped oscillators and meandering spiral waves

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 Poincaré oscillator is qualitatively identical to that for spiral waves under fixed phase control. On the other hand, under one-channel feedback control, meandering spiral waves exhibit quite different dynamic regimes appearing as specific features of a distributed system. In particular, three types of attractors (resonance, entrainment, and asynchronous) of spiral waves are observed in experiments with the light-sensitive Belousov-Zhabotinsky reaction and in numerical simulations performed for the underlying Oregonator model. A theory of the resonance attractor for meandering spiral waves is developed which predicts the attractor radius and specifies the basins of attraction in good quantitative agreement with the numerical computations and experimental observations.