Investigation of the mechanism of emergence of autowave structures at the reaction front

A qualitative mechanism for autowave pattern formation at the reaction front, observed in certain chemical systems including combustion, is suggested. It is assumed that patterns are formed as a result of interaction of two subsystems, one of which is responsible for the reaction front propagation while the other determines the formation of waves at the front. A corresponding phenomenological model is constructed in which reaction front propagation is described by a submodel of the Fisher-Kolmogorov-Petrovskii-Piskunov type and waves on the front are described by a submodel of the FitzHugh-Nagumo type. In the three-dimensional numerical analysis, it is demonstrated that the model is able to qualitatively explain the emergence of wave patterns of both spiral and target types, which are experimentally observed at the reaction front. The dependence of these patterns on the velocity and thickness of the front is examined.