Systems of "reaction-diffusion" type: signs of stability and bifurcations
Authors
M.G. Yumagulov
Ufa University of Science and Technology
N.A. Sidelnikova
Ufa University of Science and Technology
Keywords:
reaction-diffusion system, diffusion matrix, equilibrium point, periodic solution, stability, bifurcation, eigenvalues, matrix trace, boundary conditions, linear operator
Abstract
The article discusses differential equations that arise when modeling reaction-diffusion systems. Questions about the stability of equilibrium points in critical cases, as well as about bifurcations in the vicinity of such points, are studied. The conditions under which the equilibrium points of the system are stable are determined. The necessary criteria for bifurcations are obtained, under which the resulting bifurcation solutions can be stable. The main scenarios for the bifurcation behavior of the system are discussed. Examples are given to illustrate the effectiveness of the proposed approaches in problems of studying stability and bifurcations
