Dynamic Behavior Of A Predator-prey System With A Generalized Holling III Type Functional Response

Population ecology is an important branch of ecology, and predator-prey rela-tionship is one of the basic relationship between the interaction of biological pop-ulations. Since competition and predation are important parts of the biological community, and predator-prey relationship is also ubiquitous in nature, the preda-tor prey models are paid great attention by mathematicians and ecologists at home and abroad. So far the research on predator prey model has gotten rapid develop-ment. Based on this, the research on predator prey model has become a hot topic, and has important value of practical application.In this paper, we systematically study an intraguild predation system with gen-eralized Holling ?functional response. Firstly, we discuss the positivity and bound-edness of the solution, and analyze the local asymptotic stability of the boundary equilibrium, and the obtained results are verified by numerical simulation. Secondly, the equilibrium point and the global asymptotic stability of the three subsystems are analyzed, and the sufficient conditions for the global asymptotic stability are given, and some numerical simulations are carried out to support the above results. Finally, we research the persistence and extinction of every population, and obtain the sufficient criterion for the persistence and extinction of the system...