Analysis Of Nonautonomous Ratio Dependent Predator - Prey System With Avoidance

Nowadays predator-prey system has been an important research content of mathematical ecology. It has attracted much attention from many ecologists and mathematician at home and abroad. Based on this fact, we systematically investi-gate the dynamics of a nonautonomous ratio-dependent predator-prey system with prey refuge in this paper.Firstly, in the general non-autonomous case, we obtain positive invariance by using the comparison of ordinary differential equations, and give the sufficient con-ditions of the permanence and non-persistence. Also by means of the Liapunov functional method, we establish sufficient conditions of the global asymptotic sta-bility for the system. Secondly, in the periodic case, we address conditions for the existence, uniqueness and stability of a positive periodic solution by applying co-incidence degree theory. Meanwhile, we show the existence, uniqueness and global asymptotic stability of a boundary periodic solution. Thirdly, in the almost peri-odic case, we discuss the existence, uniqueness and global asymptotic stability of a positive almost periodic solution with the method which is similar to the general non-autonomous situation. Finally, we make some interesting numerical simulations using Matlab and verify our analytical findings.