Dynamics Analysis Of Predator-prey System With Ratio-dependent Holling Functional Response

In the biological population dynamics, a predator-prey system with functionalresponse has received extensive attention of scholars. Recently, some models withHolling functional response have obtained the very good study. However, there are fewof investigation on the model with Holling functional response, the ratio-dependent andrandom disturbance. Therefore, further research the model with the ratio-dependentHolling-(n+1) functional response and random perturbation is meaningful.This paper will study with ratio and random perturbations of Holling-(n+1)functional response predator-prey system related dynamics behavior.The main contentis follow as:In the first part, we study the permanence of the discrete predator-prey systemwith ratio-dependent Holling-(n+1) functional response. Considering the ratiodependent functional response of type Holling discrete predator-prey systemmathematical model, using comparison theorem and inequality technique to obtainsufficient conditions for the permanence of this system, the advance of relatedliterature.In the second part, we investigate the existence of the global positive solutions andupper bound of p-th moment of a predator-prey system with ratio-dependentHolling-(n+1) functional response and random perturbation. The model with a randomwhite noise interference, by Lyapunov function method and Ito formula, we show thatthe existence of the global positive solutions and upper bound of p-th moment.