Properties of Hopf Bifurcation in a Diffusive Population Model with Advection Term and Nonlocal Delay Effect.

The present paper is concerned with a generalized logistic reaction–diffusion–advection population model with nonlocal delay effect and subject to homogeneous Dirichlet boundary condition. Normal form of Hopf bifurcation of model at the positive steady-state solution is computed in virtue of the normal form method and the center manifold theorem for partial functional differential equations. Then the direction of Hopf bifurcation and the stability of bifurcating periodic solutions are determined in terms of the obtained normal form. It is shown that Hopf bifurcations of model at the positive steady-state solution are forward and the associated bifurcating periodic solutions are locally orbitally asymptotically stable on the center manifold. [ABSTRACT FROM AUTHOR]