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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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