一类非自治单种群阶段结构时滞模型的一致生存与全局渐近稳定性

研究了具有分布连续和离散时滞三个成长阶段的单种群模型,得到了与时滞有关的系统一致持久性的充分条件;同时通过构造Lyapunov函数得到了与时滞有关的系统全局渐近稳定的充分条件。最后由己知的文献推导出系统在持久性的条件下具有至少一个正周期解,进一步,如果系统满足全局渐近稳定的条件,则系统具有惟一全局渐进稳定的正周期解。

Uniform Endurance and Globally Asymptotic Stability for a Kind of Non-autonomous Single-species Model with Group Stage Structure and Time Delays

This paper presents a single-species model with distributed continuous and discrete time delays in which the three life stages are considered. The sufficient conditions with time delay were obtained for the uniform endurance of the system. Moreover, sufficient conditions with time delay for global asymptotic stability of the system were obtained by structuring the Lyapunov function. Lastly, according to the results in the existing references, we deduced that the system would have at least a positive periodic solution under the conditions of endurance and further, under the conditions of globally asymptotic stability, the system would have a unique positive periodic solution.