DYNAMICAL BEHAVIORS OF A STOCHASTIC PREDATOR-PREY MODEL WITH ANTI-PREDATOR BEHAVIOR

In this paper, a stochastic predator-prey model is proposed and studied, where the model has anti-predator behavior. By constructing a suit-able Lyapunov function, combined with the Ito's formula and the stochastic comparison theorem, the existence and uniqueness of the global positive solu-tion of the system are proved. Then the stochastic boundedness of the system is established, and we discussed the asymptotic behavior of the solution which fluctuates around the equilibrium point of the deterministic model. More-over, we provide sufficient conditions for the persistence and extinction of the predator and prey. Finally, the results obtained in this paper are verified by numerical simulation, and the anti-predator behavior and stochastic pertur-bation are analyzed as well.

Automated summary

In this paper, a stochastic predator-prey model with anti-predator behavior is proposed and studied. The existence and uniqueness of the global positive solution of the system are proven by constructing a suitable Lyapunov function, combined with Ito's formula and the stochastic comparison theorem. The stochastic boundedness of the system is established, and the asymptotic behavior of the solution which fluctuates around the equilibrium point of the deterministic model is discussed. Moreover, sufficient conditions for the persistence and extinction of the predator and prey are provided. Finally, the results obtained in this paper are verified by numerical simulation, and the anti-predator behavior and stochastic perturbation are analyzed as well.