Research on a Class of Predator-prey Models with Fear Effect Time Delay and Cooperative Hunting

To study the influence of fear level, fear effect time lag and the degree of cooperative hunting of predators on the dynamic behavior of the model under certain conditions,fear response delay and predator cooperative hunting were introduced into the model with fear effect. This paper studies the non-negativity and boundedness of the model solutions, the existence and stability of equilibrium points, and discusses the Hopf bifurcation at the positive equilibrium under the condition of time delay. Research shows that the fear effect, fear effect time lag, and cooperative hunting all have varying degrees of influence on the stability of the model. A higher level of fear and a relatively short time lag of the fear effect are more conducive to the stability of the model. Moderately reducing the degree of cooperative hunting can help enhance the stability of the system.