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Stability of bifurcating periodic solutions in a delayed reaction-diffusion population model. (English) Zbl 1198.37080
A delayed reaction-diffusion model of the Fisher type with a single discrete delay and zero-Dirichlet boundary conditions on a general bounded open spatial domain with a smooth boundary is considered. The stability of a spatially heterogeneous positive steady state solutions and the existence of Hopf bifurcation about this positive state solution are investigated. Using the normal form theory and the centre manifold reduction for partial functional differential equations, the stability of bifurcating periodic solutions occurring through Hopf bifurcations is investigated.
MSC:
37G05Normal forms
37G10Bifurcations of singular points
34K18Bifurcation theory of functional differential equations