主講人介紹：主要研究方向為應用動力系統及其在復雜生物系統的應用。論文發表在《SIAM J. Appl. Math.》、《J.Diff. Equ.》、《J.Theor.Biol》、《J.Math.Biol.》、《Bull.Math. Biol.》、《J. Nonlinear Sci.》、《Scientific Reports》等應用數學以及理論生態學雜志。近年來對具有季節驅動或年齡結構的復雜系統以及復雜網絡上的疾病傳播動力學感興趣。近期研究受國家自然科學基金和香港特別行政區大學教育資助委員會資助。
內容介紹：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.