Science supervisor: Prof. Dr. A. Loskutov.
At the present, numerous applications of nonlinear dynamics attract widespread attention. This is due to the fact that methods which are developed in the theory of dissipative systems can be successfully used for solution of old problems including information processing, description of excitable media and self-organisation phenomena, etc. In our group one of the investigation lines is analysis of nonlinear oscillative systems, including chaotic phenomena. As known, chaos is a widespread phenomenon. Chaotic behaviour is brought about the complexity of the system.
The most known oscillating chemical reaction which can exhibit various dynamical regimes (periodic, quasiperiodic, diffusive-induced chaotic, and chaotic) is the Belousov reaction. This reaction has been discovered at the very beginning of 50-s. It should be noted that oscillating chemical reactions were known before. But there were no explanations to these facts, and most researches supposed that pure chemical oscillations are impossible. It was B.P. Belousov work, that gave start to the modern history of their systematic study.
Chaotic dynamics in oscillating chemical reactions can appear as a result of nonlinearity of the mass-action law (for the spatially homogeneous media) and due to the diffusion processes. In the latter case, in the absence of stirring of reaction mixture, oscillating reactions is be accompanied by diffusion. This leads to formation of various spatial heterogeneities and patterns (for example, chemical waves). To describe such a mixture it is necessary to take into account spatial coordinates and to employ partial differential equations. This approach leads to sufficient complication of the analysis of the dynamical regimes and, as a rule, can be realized only numerically.
One of the most interesting problems in application to heterogeneous chemical systems is controlling and suppression their spatio-temporal chaotic behaviour. Nowadays, there are many ways of the stabilisation of chaotic dynamics. One of them is used in our investigations to suppress the diffusive-induced chaos in the Field-Koeroes-Noyes spatial model of the Belousov reaction.