Dynamics of a controlled discrete prey-predator model with Holling type-II functional response

This article investigates the complex dynamic behavior of a discrete predator-prey model with Holling type II functional response. Firstly, we discuss the local stability of the system at the equilibrium points. Secondly, we use the central manifold theorem and bifurcation theory to prove that two different types of bifurcations in the system, namely flip bifurcation and Hopf bifurcation. Through numerical simulation, we validate the impact of human control parameters of predators and the degree of predator utilization on system dynamics. The results indicate that studying the predator-prey relationship between species in plateau pastoral areas can help humans better predict the population changes of prey and predator, and have great significance for the protection of ecosystems.