Dynamics of two species predator-prey model with spatially nonhomogeneous diffusion strategy - Ma, Li; Liang, Haihua; Wang, Huatao (Journal of mathematical analysis and applications, 2025)
In this paper, we investigate a Holling type-II predator-prey system with spatially nonhomogeneous diffusion strategy. By employing the methods of the implicit function theorem, eigenvalue theory and bifurcation theory, we analyze the stability/instability of the positive steady state and explore the existence of a Hopf bifurcation when the diffusion rate is large. Furthermore, when the driven diffusion functions Q1(x)=eqm(x) and Q2(x)≡1, we detailed discuss how the parameter q of the density dependent diffusion Q1(x) affect the occurrence of Hopf bifurcations and the values of Hopf bifurcations.