学 术 报 告一

报告题目：Effect of impulsive controls in a model system for age-structured population over a patchy environment

报 告 人：杨志春教授 (重庆师范大学)

报告时间：2019年3月26日（星期二）下午 3：00—4：00

报告地点: 应用数学研究中心报告厅（计算机楼718#）

摘要： In this talk, a model of impulsive delay differential equations in n-patches is rigorously derived to describe the impulsive control of population of a single species over n-patches. The model allows 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: (1) without impulsive control; (2) with impulsive culling of the immatures only; and (3) 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.

报告人简介: 杨志春，男，博士，教授，重庆市巴渝学者，重庆市高校创新团队负责人。主要从事微分方程与控制论研究，包括泛函微分方程、脉冲系统与混合控制、复杂网络与神经网络、生物数学等领域。先后主持国家自然科学基金面上项目2项、省部级项目近10项，参加省部级及以上项目10余项。与他人合作成果在IEEE 汇刊（自动控制、电路与系统)、J Math. Biol.等刊物上发表论文70余篇，成果获重庆市自然科学奖三等奖2项。

学 术 报 告二

报告题目：Differentiability of the conjugacy in the Hartman-Grobman Theorem

报 告 人：张文萌教授 (重庆师范大学)

报告时间：2019年3月26日（星期二）下午 4：00—5：00

报告地点: 应用数学研究中心报告厅（计算机楼718#）

摘要： The classical Hartman-Grobman Theorem states that a C^1 diffeomorphism near its hyperbolic fixed point is topological conjugate to its linear part. In general, this conjugacy is not smooth, not even Lipschitz continuous. In this talk, we show that for a C^1 diffeomorphism with Holder continuous derivative, the conjugacy is differentiable at the fixed point. We also give a counter example showing that the regularity condition cannot be lowered to only C^1. This is a joint work with Prof. Kening Lu and Prof. Weinian Zhang.

报告人简介: 张文萌，重庆师范大学教授，硕士生导师。分别于2011年和2012年在波兰绿山大学和四川大学取得博士学位，从2012年开始在重庆师范大学数学科学学院工作，主要从事的研究领域为微分方程与动力系统，重点关注其中的线性化与不变流形等问题。近年来，在该研究领域取得一系列重要成果，在美国Trans. Amer. Math. Soc.、Adv. Math.、Math. Ann.等期刊上发表论文14篇。先后主持国家自然科学基金面上项目和青年项目等省部级以上项目6项，参与国家自然科学基金重点项目1项，部分成果获2018年度教育部自然科学一等奖（排名第2），并入选重庆市第四批高层次人才特殊支持计划（科技创新领军人才）。