报告题目：Dynamics of systems with nested invariant cones: non-autonomous case

报告人：周盾副教授，南京理工大学

报告时间：2024年1月19日（周五）9:30-10:30

报告地点：腾讯会议 392-182-919，参会密码请联系夏永辉

报告摘要：Monotone dynamical systems are mainly concerned with the dynamics of typical orbits. To investigate dynamics of those minority orbits, some other conditions are often needed, such as nested invariant cone structure. In this talk, under the frame of nested invariant cones, dynamics of almost-periodic systems and its’ $C^1$ perturbations are investigated. In particular, we prove that any omega-limit set generated by the skew-product semiflow of perturbed system contains at most two minimal sets, and any minimal set is an almost automorphic extension of its base flow(a universal phenomenon in multi-frequency driven systems). As some applications of our results, we consider scalar parabolic equations with separated boundary conditions under small non-local perturbations and well known competitive-cooperative tridiagonal systems with small perturbations.

报告人简介：周盾，南京理工大学副教授，硕士生导师。主要研究兴趣为：单调动力系统，无穷维动力系统，非自治动力系统。先后主持中国博士后基金面上，国家自然科学基金青年项目，面上项目，参与国家自然科学基金重点项目。相关研究成果发表在J. Differential Equations，Science China Mathematics，Journal of Mathematical Biology，Proc. Amer. Math. Soc., J. Dynam. Differential Equations等国际权威数学杂志上。

报告题目：Statistical Behavior of Monotone Dynamical System

报告人：张裕烽，苏州大学博士后

报告时间：2024年1月19日（周五）10:30-11:30

报告地点：腾讯会议 392-182-919，参会密码请联系夏永辉

报告摘要：In this talk, we consider about the statistical behavior of monotone dynamical systems, including prevalent behavior and Birkhoff center. We will show that the prevalent orbits convergent to cycles for classical strongly monotone discrete-time systems; the prevalent orbits will be pseudo-ordered or convergent to equilibria for smooth flows with invaraint cones of rank k; the order structure of Birkhoff center of strongly competitive flows.

报告人简介：张裕烽博士，毕业于中国科学技术大学，现于苏州大学作博士后。主要研究方向为单调动力系统。相关成果发表在JDDE、PAMS等杂志上。现主持2项项目，分别为博士后特别资助项目（站前）和博士后面上项目。