Symmetry-breaking bifurcations in a delayed reaction–diffusion equation.

This paper is concerned with a delayed reaction–diffusion equation on a unit disk. By means of the singularity theory and Lyapunov–Schmidt reduction, we not only derive universal conclusions about the existence of inhomogeneous steady-state solutions and the equivariant Hopf bifurcation theorems, but also obtain some more extraordinary properties of bifurcating solutions, which are produced by the radial symmetry through abstract methods based on the Lie group representation theory. Meanwhile, we illustrate our results by an application to a population model with a time delay. Furthermore, the methods established in this paper are applicable to specific delayed reaction–diffusion models with other symmetries. [ABSTRACT FROM AUTHOR]