On the Gause type prey-predator model with variable mortality rate for the predator

Abstract

In this thesis, a general predator-prey model (2.16) with a variable mortality rate was con- sidered under H -H assumptions. The qualitative study of model shows the possibility of the existence of at least one positive equilibrium point E× (x×, y×) in addition to the bound- ary equilibria E and E (K, Under conditions of existance of a positive equilibrium E× (x×, y×) , the two privious equilibria are saddle point. Local stability properties are given in theorem On the other hand, some global asymptotic stability and non-existence of limite cycle conditions are given by different methods in section and By considering a logistic growth function and Holling II functional response in all examples of chapter 3, we have applied our exstension RMA criterion to show graphicaly the exponential stability of a positive equilibrium point. In essence, the primary objective of this research is to showcase instances where such stability can be observed, even if the positive equilibrium lies on ascending branch of the prey isocline, in contrast to the expectations set by the RMA model for which the equilibrium is LES if and only if it is located on a descending branch of this isocline