Globally asymptotical stability and existence of limit cycle for a generalized predator-prey model with prey refuge

摘要

The stability property of the positive equilibrium and the existence of limit cycles for the Lotka-Volterra predator-prey system incorporating prey refuge with a generalized functional response are investigated. On the one hand, by constructing a suitable Lyapunov function and an auxiliary system, a new set of sufficient conditions which guarantee the global asymptotical stability of the positive equilibrium are obtained. On the other hand, a set of sufficient conditions which guarantee the existence of limit cycles are produced by modifying the theorem of Hesaaraki and Moghadas. Our results complement and supplement some known ones, and some published conclusions become the special cases of ours.