Abstract:

In this talk, we will show the existence and stability of the spatially inhomogeneous periodic solutions for some diffusive population models subject to Dirichlet or Neumann boundary conditions. For the Dirichlet boundary condition problem, we demonstrate that the spatially inhomogeneous periodic solutions can be bifurcated from the positive steady state for both Logistic and weak Allee type population models. For a special Logistic type model, such bifurcated periodic solutions are shown to be persistent when the parameter is far away from the bifurcation values. For the Neumann boundary condition problem, we establish the existence of various spatially inhomogeneous periodic solutions for the diffusive Nicholson’s blowflies population model. Such periodic solutions are numerically observable in a relatively long time period although they are not stable. This talk is mainly based on some joint works with Junping Shi, Junjie Wei and Xingfu Zou.