Dynamics of a stochastic predator-prey model with fear effect and hunting cooperation

To explore the relationship between hunting of predator and anti-predation behavior of prey in the natural environment, considering a stochastic predator-prey model with fear effect and hunting cooperation, which is perturbed by the nonlinear white noise. Firstly, the relevant properties of solutions for the model are studied. Then, we present sufficient conditions for extinction, persistence, and stationary distribution. Especially, the density function near positive equilibrium of model without white noise is established. Finally, based on the results of numerical simulation and theoretical analysis, it is revealed that fear effect, hunting cooperation, and white noise have indispensable influence on the dynamical behaviors of this model.