Dynamical analysis of a predator-prey system with Hassell-Varley-Holling functional response. (Chinese. English summary) Zbl 1247.92058

Zhong, Minling; Liu, Xiuxiang

Acta Math. Sci., Ser. A, Chin. Ed. 31, No. 5, 1295-1310 (2011).

Summary: This paper deals with a non-autonomous predator-prey system with Hassell-Varley-Holling functional response. The permanence and extinction are considered for the general non-autonomous case. For the periodic (almost periodic) case, necessary and sufficient criteria for the existence of positive periodic (almost periodic) solutions are derived by a new estimation technique and the invariance property of homotopy. The dynamics of boundary periodic (almost periodic) solutions are also investigated. The authors end this paper with some numerical simulations and interesting remaining problems.

MSC:

92D40	Ecology
34C25	Periodic solutions to ordinary differential equations
34C27	Almost and pseudo-almost periodic solutions to ordinary differential equations
65C20	Probabilistic models, generic numerical methods in probability and statistics

Keywords:

permanence; extinction; periodic solutions; almost periodic solutions