A Delayed Succession Model with Diffusion for the Impact of Diapause on Population Growth

主讲人：Yijun Lou，香港理工大学教授

时间：2019年11月18日8：00

地点：3号楼301室

举办单位：数理学院

主讲人介绍：主要研究方向为应用动力系统及其在复杂生物系统的应用。论文发表在《SIAM J. Appl. Math.》、《J.Diff.  Equ.》、《J.Theor.Biol》、《J.Math.Biol.》、《Bull.Math. Biol.》、《J. Nonlinear  Sci.》、《Scientific  Reports》等应用数学以及理论生态学杂志。近年来对具有季节驱动或年龄结构的复杂系统以及复杂网络上的疾病传播动力学感兴趣。近期研究受国家自然科学基金和香港特别行政区大学教育资助委员会资助。  

内容介绍：Diapause, a period of arrested development driven by adverse environmental  conditions, plays an important role on the establishment and invasion of insects  and other invertebrate organisms in temperate and subtropical areas. In order to  describe the spatial dynamics of diapausing species, we propose a novel model  involving (a) seasonal succession to distinguish the normal growth period,  diapause period, and post diapause period; (b) diffusion term to represent the  random movement of species; and (c) maturation delay term to describe the Dirac  distribution for the residence time in the immature stage. To investigate the  survival and establishment of a species, we first study the model in a bounded  domain. The extinction and persistence of the species can be predicted by the  basic reproduction ratio. Furthermore, the model in an unbounded domain is  investigated to analyze the spreading of the species. The existence of the  minimal wave speed for traveling wave solutions and its coincidence with the  spreading speed are established. Numerical simulations are performed to validate  theoretical results, and in particular to compare the effects of two diapausing  strategies, diapausing in the adult stage and in the immature stage.