Stability and Hopf bifurcation in a prey-predator model with memory-based diffusion

<p style='text-indent:20px;'>In this paper, we consider a predator-prey model with memory-based diffusion. We first analyze the stability of all steady states in detail. Then by analyzing distribution eigenvalues, find that average memory period can cause change positive state, and Hopf bifurcation occurs at state. Moreover, from central manifold theorem normal form theory, give direction bifurcation. The results show that, under certain conditions, family spatially inhomogeneous periodic solutions will bifurcate state when appear.</p>