Wawelet transform application for classification of solutions of reaction-diffusion systems

Abstract

Girer–Meynxardt type system of reaction-diffusion with classical derivatives and Bryusselyator system with fractional time derivatives are investigated. On the basis of computer simulations it is shown that qualitatively different types of oscillatory solutions may arise due to instability in these systems. Wavelet transformations are applied to analyze and classify the solutions of such systems, A comparative estimation of wavelet transforms of oscillatory and chaotic solutions is given and it is shown that such method of classification of solutions is effective.