A Predator-Prey Model In Deterministic And Stochastic Environments

We investigate the phase portraits, the uniqueness of limit cycles and the Hopf bifurcations in the Holling-Tanner models in deterministic and stochastic environments. We provide the conditions on the parameters to assure saddle, focus and node. We use numerical simulations to demonstrate our results in the deterministic cases. We also explore the Holling-Tanner model in a stochastic environment by using numerical simulations. We generalize and improve some new results on Holling-Tanner model from Lotka-Volterra model on real ecological systems.