Gichan O. Nonequilibrium patterns of reaction-diffusion systems of activator-inhibitor type

3. The research object was processes of self-organizing, which occur in reaction-diffusion systems far from thermodynamic equilibrium. On the basis of methods of the theory of dynamic systems and the theories impedance spectroscopy the conditions of occurrence and feature of development of nonequilibrum patterns in two such systems were obtained. For the first system - the FitzHugh-Nagumo model (FHN) the conditions of occurrence of low dimentional spatial and temporal structures under the Hopf and Turing instabilities are established. The full version of the FHN model in its 0-dimentional, one-dimensional and two-dimentional cases were considered. The results are expressed through parameter of external force, that is considered as an opportunity of the external control of the system behaviour and the occurrence in it diferent type of structures. For the second model system - the electrochemical system with electrocatalic reaction on a surface of a spherical microelectrode in potentiostatic conditions the frequencies under which the Hopf bifurcation arises are calculated. The influence on these bifurcation frequencies in dependance of the sizes of a spherical electrode and thickness of the Nernst diffusion layer is established.