| The present paper is concerned with the Holling type IV predator-prey diffusion system with Neumann boundary condition.In order to investigate the stability of the positive equilibrium,the system at the positive equilibrium is linearized and the associated characteristic equation is analyzed,and then the asymptotic stability of the positive equilibrium is obtained.By analysis,we show that the positive constant steady state of the system without delay is stable in some interval.However,the constant steady state loses stability when the delay increases cross certain values in the delayed predator-prey system.Finally,the bifurcation direction and stability of the bifurcating periodic solution are considered. |
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