Ways of investigation of autowave systems

Abstract

We do not use the word “methods” in the title of this section since we wish to emphasize that a qualitative theory of AW processes is still to be constructed. This can be illustrated by comparing the undeveloped approaches used for studying AW systems with the state-of-the-art investigation of the nonlinear systems of the second order whose behaviour in thé parameter space is known in ample detail. So far, only some particular, though rather important, cases have been considered. However, qualitative and computer methods for studying AW processes simulated by parabolic quasilinear equations seem to be promising. The point is that it is sufficient to take into account a finite (usually small) number of degrees of freedom. Therefore the main problem which arises in analyzing AW processes, is to recognize these several degrees of freedom, to find stationary solutions, and to investigate their stability and transitions between them.