Publication date: 2021

DOI: 10.1134/S1995080222030027

The problem of the first Lyapunov quantity constructing on the Andronov-Hopf bifurcation problem in infinite-dimensional dynamical systems is considered. A general scheme of obtaining new formulas for the Lyapunov quantity in terms of the original equations is proposed. The ''reaction-diffusion'' equation in a limited region and in a situation when there are no flows of reacting components across the boundary of the region is considered as the main object of research. For this equation, the Andronov-Hopf bifurcation conditions in the vicinity of a spatially homogeneous equilibrium point are obtained, necessary conditions for the stability of emerging solutions are specified. New formulas for the first Lyapunov quantities and transcriticity indices of the problem, leading to algorithms for constructing these quantities are proposed. The specifics of these formulas are indicated in the situation when the nonlinearity begins with cubic terms. The proposed formulas make it possible not only to efficiently calculate the Lyapunov quantities, but also to conduct a study of the properties of bifurcations in reaction-diffusion systems under new conditions.

Издатель: MAIK NAUKA/INTERPERIODICA/SPRINGER233 SPRING ST, NEW YORK, NY 10013-1578

Тип: Article