A New Perturbation Approach to Highly Nonlinear Chemical Oscillation with Diffusion Process

We present in this short note a simple perturbation scheme to derive a reduced description of the dynamics of reaction-diffusion systems deep in a temporally ordered state. This work was motivated by Ortoleva and Ross' phase-wave theory of heterogeneous reaction-diffusion system in which the degree of heterogeneity is taken as a small parameter.!) In contrast to their work, however, we consider a homogeneous system and the amplitude and the instantaneous frequency are expanded in powers of spacederivatives. We restrict our consideration to a twocomponent reaction -diffusion system because in this case one may give an explicit definition of phase and amplitude so that the theory may be developed in a most unambiguous way. We start with the equations