Vasjunyk Z. Mathematical modelling of nonstable spatially-inhomogeneous structures in reaction-diffusion systems

The dissertation is devoited to research of non-uniform solutions which are realized in concrete reaction-diffusion systems. These solutions have a form of a kind dissipative structures and chaotic fluctuations. Aim of dissertation is a study of decisions and internal laws of such systems, working out of a new approaches to en estimation of a randomness of decisions. A small parameter methods is generalized for a reaction-diffusion system where deviation from the critical value of bifurcation parameter is taken as a small parameter, The analytical substantiation of existence global attractor in the case of performance of condition of the Hopf theorem carried out. The bifurcation diagram which considers secondary Hopf bifurcation are constructed. New approaches for an estimation of a randomness of solution are approved on the basis of wavelet-transform, method of visualization of the data and calculation fractal dimensions of solution projection on a plane.