Analysis of a delayed predator-prey system with Holling type-IV functional response and impulsive diffusion between two patches

Abstract

Due to the extensive existence of time delay for natural population, it is necessary to take the effect of time delay into account in forming a biologically meaningful mathematical model. In view of this, a delayed predator-prey system with Holling type-IV functional response and impulsive dispersal between two patches is formulated. By using comparison theorem of impulsive differential equation and some analysis techniques, we obtain a predator-extinction periodic solution, which is globally attractive. Furthermore, it is proved that the investigated system is permanent. Numerical simulations are carried out to illustrate the theoretical results.