## Global stability of Gause-type predator-prey systems.(English)Zbl 0742.92022

The following class of Gauss-type predator-prey models is considered $x'=xg(x)-\xi(y)p(x),\qquad y'=\eta(y)(-\gamma + q(x)),(1)$ where $$x(t)$$ amd $$y(t)$$ represent the prey and predator populations, respectively. The main aim of this paper is addressed to obtaining sufficient conditions under which the system (1) has a global asymptotically stable nontrivial equilibrium solution. Results are obtained via comparison techniques and Bendixson-Dulac’s criterion.
Reviewer: M.Lizana (Caracas)

### MSC:

 92D40 Ecology 34D05 Asymptotic properties of solutions to ordinary differential equations 34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
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