具有时滞与生理阶段结构的竞争捕食-被捕食系统的正周期解

Positive Periodic Solutions of a Competitive Predator-prey System with Delays and Stage-structure

运用重合度理论与Lyapunov泛函方法为一类具有时滞与生理阶段结构的竞争捕食-被捕食系统正周期解的存在性和全局吸引性提供了新的判别准则.文中利用积分中值定理将积分方程转换为代数方程,为拓扑度的计算提供了新的技巧;并讨论了时滞、阶段结构和竞争因素对系统正周期解的存在性和全局吸引性的影响;最后举例说明了文中的存在性条件比已有结论更简洁、全局吸引性的判别准则也是新的.

By using Coincidence Degree Theorem and constructing a Lyapunov functional, new criteria are presented for the existence and global attractivity of positive periodic solu- tions of a competitive predator-prey system with delays and stage-structure. In this paper, we provide a new technique of caculation on topologic degree by transforming an integral equations into an algebraic one. Moreover, what the delays and stage-structure and competition affect on the existence and global attractivity of positive periodic solutions is discussed. Finally, an example is cited to illustrate that the existence conditions in this paper are more concise and the criterion for the global attractivity is also new.