Analysis Of A Non-autonomous Predator-prey System With Ratio-dependent Holling-? Functional Response

With the in-depth study of ecology,the predator model with functional response has been paid more and more attention,and has become one of the important research contents of ecology and biomathematics.Based on this,This article will systematically analyze the nature of such a system.First,for the case where the system parameters are generally non-autonomous,the final bounded region and the positive invariant set of the system and the conditions for their existence are obtained,and the discrimination conditions that must be met for the system to continue are given,and the method obtains the condition that any arbitrary positive solution of the system is globally asymptotically stable;secondly,for the case where the system parameters are periodic functions,Using the continuation theorem of coincidence degree,we obtain the conditions that the system needs to satisfy at least one positive periodic solution,and prove that the solution is globally asymptotically stable under appropriate conditions;again,for the case where the system parameters are almost periodic functions,With the help of the proof method in Chapter 2,we obtain the conditions that the system needs to be unique and globally asymptotically stable positive almost periodic solution.Moreover,for each case,the numerical simulation through Matlab proves that the conclusion is correct.