COMPLEX ORDERING AND STOCHASTIC-OSCILLATIONS IN A CLASS OF REACTION-DIFFUSION SYSTEMS WITH SMALL DIFFUSION

We consider four models of partial differential equations obtained by applying a generalization of the method of normal forms to two-compone nt reaction-diffusion systems with small diffusion u(t) = epsilon Du(x x) + (A + epsilon A(1))u + F(u), u epsilon R(2). These equations (quas inormal forms) describe the behaviour of solutions of the original equ ation for epsilon --> 0. One of the quasinormal forms is the well-know n complex Ginzburg-Landau equation, The properties of attractors of th e other three equations are considered. Two of these equations have an interesting feature that may be called a sensitivity to small paramet ers: they contain a new parameter theta(epsilon) = -(a epsilon(-1/2) m od 1) that influences the behaviour of solutions, but changes infinite ly many times when epsilon --> 0. This does not create problems in num erical analysis of quasinormal forms, but makes numerical study of the original problem involving epsilon almost impossible.