Spiral waves and dissipative solitons in weakly excitable media

Abstract

Spiral waves are among the most prominent examples of spatio-temporal patterns in various excitable media, including heart muscle, the retina of the eye, social amoeba colonies and the chemical Belousov-Zhabotinsky reaction. Recent studies have shown that, in addition to spiral waves, there is another possible waveform, viz. a propagating wave segment that is stationary in size and shape. Such localized spatio-temporal structures in nonlinear dissipative media exhibit all the basic features of dissipative solitons. In this chapter, a free boundary model is presented to describe the shape and velocity of the wave segments. It turns out that a generalization of this model allows us to determine the shape and angular velocity of a spiral wave that is rotating rigidly in a medium of low excitability. Thus, our study demonstrates that dissipative solitons (propagating wave segments) and spiral waves are closely connected to each other and that they represent different solutions in the framework of a common theoretical model. © 2008 Springer-Verlag Berlin Heidelberg.