报告题目：Non-autonomous Discrete Dynamical Systems and Applications to Biology
报告时间：2019年7月6日，星期六，上午09:40-10:40
报告地点：数学楼2-3会议室
报告人: Prof. Saber N. Elaydi，Trinity University
Abstract:
We consider a discrete non-autonomous semi-dynamical system generated by a family of continuous maps defined on a locally compact metric space. It is assumed that this family of maps uniformly converges to a continuous map. Such a non-autonomous system is called an asymptotically autonomous system. We extend the dynamical system to the metric one-point compactification of the phase space. Our study will be applied to a special class of maps, triangular maps. This is done via the construction of an associated skew-product dynamical system. We prove, among other things, that the omega limit sets are invariant and invariantly connected. We apply our results to three populations models, the Ricker model with no Allee effect, Elaydi-Sacker model with the Allee effect, and the 2-species hierarchical competition Ricker model with the Allee effect, where it is assumed that the reproduction rates change with time due to habitat fluctuation.
报告人简介：
Saber N. Elaydi老师是美国得克萨斯州Trinity University教授。1978年毕业于哥伦比亚密苏里大学数学系，获博士学位，曾在加州大学伯克利分校访问，曾任科威特大学和凯斯西储大学助理教授。2017年获Aulbach 终身成就奖。研究领域包括离散动力系统、差分方程、生物数学、数学神经科学及数学经济学等。先后主持多项美国自然科学基金项目，出版专著3本。现任Journal of Difference Equations and Applications (JDEA)总编辑、Journal of Biological Dynamics的共同主编、任Journal of Dynamics and Games, PLoS ONE等杂志的编委，同时也是Advances in Discrete Mathematics and Applications系列著作的编委。多次做大会报告，为离散生物动力系统的研究和推广做出了重要贡献。是国际离散生物数学领域有影响的专家。
