Bifurcation analysis of a diffusive predator–prey system with nonconstant death rate and Holling III functional response

•A diffusive predator–prey system with nonconstant death rate and Holling III functional response is considered.•The stability of equilibria and Turing instability of the positive equilibrium are obtained.•The detailed Hopf bifurcation analysis to PDE system is presented.

In this paper, a diffusive predator–prey system with Holling III functional response and nonconstant death rate subject to Neumann boundary condition is considered. We study the stability of equilibria, and Turing instability of the positive equilibrium. We also perform a detailed Hopf bifurcation analysis to PDE system, and derive conditions for determining the bifurcation direction and the stability of the bifurcating periodic solution. In addition, some numerical simulations are carried out.