Stability and Hopf Bifurcation for a Population Delay Model with Diffusion Effects

where # C([&r, 0], H 0[0, ?]), k>0 and r>0 are constants. Related problems with Neumann boundary conditions or on an unbounded domain have also been studied by [1], [3], [11 18]. However, in these cases there always exist nontrivial spatially constant solutions, and it is the stability of these solutions and bifurcations about them that are treated. Such nontrivial constant solutions do not exist in the present problem with Dirichlet conditions, and the first bifurcation that needs to be addressed concerns the existence, uniqueness and stability of a feasible (non-negative) equilibrium.

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