Predator-prey System Analysis With Crowley-Martin Type Functional Response

In this paper, we systematically study the dynamics of a nonautonomous predator-prey system with Crowley-Martin functional response.Firstly, in the general non-autonomous case, we establish the criterions for the permanence and non-persistence of the system. Meanwhile, by constructing a suitable Liapunov function, sufficient conditions of global asymptotic stability of positive solutions are given. Secondly, in the periodic case, by applying the continuation theorem of coincidence degree theory, a sufficient condition is obtained for the existence, uniqueness and stability of a positive periodic solution. Moreover, we also explore the existence, uniqueness and global asymptotic stability of a positive boundary periodic solution. Thirdly, in the almost periodic case, we obtain the sufficient conditions of the existence and uniqueness of almost periodic solutions by using the method which is similar to the general non-autonomous situation. Finally, we perform numerical simulations by using Matlab to show our analytical findings.