In this talk, I will present a very general model of impulsive delay differential equations in $n-patches$ that describe the impulsive control of population of a single species over $n-$patches. The model has an age structure consisting of immatures and matures, and also considers mobility and culling of both matures and immatures. Conditions are obtained for extinction and persistence of the model system under three special scenarios: (i) without impulsive control; (ii) with impulsive culling of the immatures only; and (iii) with impulsive culling of the matures only, respectively. In the case of persistence, the persistence level is also estimated for the systems in the case of identical $n$ patches, by relating the issue to the dynamics of multi-dimensional maps. Two illustrative examples and their numerical simulations are given to show the effectiveness of the results. Based on the theoretical results, some strategies of impulsive culling are provided to eradicate the population of a pest species.
星期五, 2018/10/05 - 从 15:00 到 17:00