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Global asymptotical stability of the positive equilibrium of the Lotka-Volterra prey-predator model incorporating a constant number of prey refuges. (English) Zbl 1254.92073

Summary: We investigate the stability property of the positive equilibrium for Lotka-Volterra predator-prey systems incorporating a constant number of prey refuges. By constructing a suitable Lyapunov function, a set of sufficient conditions which ensure the global asymptotical stability of the positive equilibrium is obtained. Our result complements and supplements some known ones.

MSC:

92D25 Population dynamics (general)
34D20 Stability of solutions to ordinary differential equations
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