Positive periodic solutions of a delayed predator-prey system with Holling type II functional response and stage structure for predator. (Chinese. English summary) Zbl 1106.34042
Summary: By using a continuation theorem based on Gaines and Mawhin’s coincidence degree, the authors study the global exisence of positive periodic solutions of a delayed predator-prey system with Holling-II-type response and stage structure for the predator. A set of easily verifiable sufficient conditions is obtained, which improves some known results. Also, by constructing a suitable Lyapunov function, sufficient conditions, which guarantee the global attractivity of the positive periodic solution, are obtained.
MSC:
34K13 | Periodic solutions to functional-differential equations |
34K20 | Stability theory of functional-differential equations |
92D25 | Population dynamics (general) |