Dynamics of spiral waves in non-equilibrium media

A class of non-equilibrium media described by equations close to gradient one is considered. For the analysis of the field structure dynamics in such media an asymptotic method is proposed where the generating solution is that of the gradient system. The analysis is based on the generalised Ginzburg-Landau equation. For in =O this equation can be written as delta a/ delta t=- delta F(a)/ delta a* where F is the Lyapunov functional: F=(f( mod a mod ²)+ mod a mod ²) dx dy and solutions are possible in the form of static spiral waves centred on the point (x, y). When O( in <<1 a solution is sought in the form of an asymptotic series with the first term having the form of a spiral wave, but the parameters x, y and phase will be slow functions of time. Using this method the interaction of a pair of spiral waves in media with hard and soft excitation is investigated and the stochastic drift of a spiral wave in a periodically inhomogenous field is predicted.