Global dynamics of a predator-prey model |
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Authors: | Xiuxiang Liu Yijun Lou |
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Affiliation: | a School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, PR China b Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NL A1C 5S7, Canada |
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Abstract: | This paper deals with the dynamics of a predator-prey model with Hassell-Varley-Holling functional response. First, we show that the predator coexists with prey if and only if predator's growth ability is greater than its death rate. Second, using a blow-up technique, we prove that the origin equilibrium point is repelling and extinction of both predator and prey populations is impossible. Third, the local and global stability of the positive steady state coincide when the predator interference is large. Finally, for a typical biological case, we show instability of the positive equilibrium implies global stability of the limit cycle. Numerical simulations are carried out for a hypothetical set of parameter values to substantiate our analytical findings. |
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Keywords: | Predator-prey model Predator-dependent response Coexistence and extinction Complicated equilibrium Global stability Uniqueness of limit cycles |
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