Interference patterns in spiral wave drift induced by a two-point feedback.

The drift velocity field describing spiral wave motion in an excitable medium subjected to a two-point feedback control is derived and analyzed. Although for a small distance between the two measuring points a discrete set of circular shaped attractors are observed, an increase of induces a sequence of global bifurcations that destroy this attractor structure. These bifurcations result in the appearance of smooth unrestricted lines with zero drift velocity, similarly to zero intensity lines under destructive interference in linear optics.

Global control of spiral wave dynamics in an excitable domain of circular and elliptical shape.

Experiments performed in a thin layer of the Belousov-Zhabotinsky solution subjected to a global feedback demonstrate the existence of the resonance attractor for meandering spiral waves within a domain of circular shape. In an elliptical domain, the resonance attractor can be destroyed due to a saddle-node bifurcation induced by a variation of the domain eccentricity. This conclusion explains the experimentally observed anchoring of spiral waves at certain points of an elliptical domain and is in good quantitative agreement with numerical data obtained for the Oregonator model.

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.

Oscillatory dispersion and coexisting stable pulse trains in an excitable medium.

For planar wave trains in excitable media, we found a novel type of anomalous dispersion distinguished by bistable domains in the dependence of the propagation velocity on the wavelength. Within one medium alternative stable pulse trains can coexist having the same wavelength but different velocities. The phenomenon is related to oscillatory recovery of excitations, which causes small amplitude oscillations in the refractory tail of pulses.