Periodicity in a generalized semi-ratio-dependent predator–prey system with time delays and impulses

With the help of a continuation theorem based on coincidence degree theory, we establish necessary and sufficient conditions for the existence of positive periodic solutions in a generalized semi-ratio-dependent predator–prey system with time delays and impulses, which covers many models appeared in the literature. When the results reduce to the semi-ratio-dependent predator–prey system without impulses, they generalize and improve some known ones.     

一个离散的比率依赖Holling-Ⅲ捕食-食饵系统的持久性

本文研究了一个带有Holling-Ⅲ类功能反应和时间延迟的离散半比率依赖捕食-食饵系统,得到了该态系统永久持续生存的充分条件。     

Existence of positive periodic solutions for an impulsive semi-ratio-dependent predator-prey model with dispersion and time delays

In this paper, we propose an impulsive semi-ratio-dependent predator-prey model with dispersion and time delays. By applying the continuation theorem of coincidence degree theory, we establish a set of sufficient conditions on the existence of at least one positive periodic solution. The result not only improves but also generalizes that for the case without pulses.