The stability of Holling type IV predator-prey system with and without delay

The present paper is concerned with the Holling type IV predator-prey system with diffusion. By analyzing the characteristic equation associated with the positive equilibrium, the conditions for the asymptotic stability of the positive equilibrium is obtained. For the system without delay, it has been shown that the positive equilibrium is stable in certain region of the parameter plane. However, the introducing of the delay can lead to the loss of the stability. We find that in the region where the positive equilibrium is stable for the system without delay, there exists a critical value of the delay and the positive equilibrium is stable when the delay is less than this critical value and becomes unstable when the delay is greater than it. Copyright © 2012 by Editorial Board of Journal of Donghua University, Shanghai, China.