報告承辦單位:數(shù)學(xué)與統(tǒng)計學(xué)院

報告內(nèi)容: Spectral Monotonicity of Perturbed Quasi-positive Matrices with Applications in Population Dynamics

報告人姓名:吳毅湘

報告人所在單位:美國中田納西州立大學(xué)

報告人職稱:助理教授，博士

報告時間: 2020年1月8日下午4:30

報告地點: 云塘校區(qū)理科樓A-419

報告人簡介：吳毅湘,博士,于2010年在中南大學(xué)獲得理學(xué)學(xué)士學(xué)位，于2015年在美國路易斯安那大學(xué)獲得理學(xué)博士學(xué)位。2015年7月至2016年8月在加拿大西安大略大學(xué)從事博士后研究。2016年9月至2019年7月，任美國范德堡大學(xué)助理教授(非終身制)。2019年8月，任美國中田納西州立大學(xué)助理教授。目前，研究興趣主要是反應(yīng)擴(kuò)散方程和生物數(shù)學(xué)。其研究成果已在《Nonlinearity》，《SIAM Appl Math》，《Bull Math Biology》，《J. Differential Equations》等國際數(shù)學(xué)雜志上發(fā)表論文10余篇。

報告摘要：Threshold values in population dynamics can be formulated as spectral bounds of matrices, determining the dichotomy of population persistence and extinction. For a square matrix $\mu A + Q$, where $A$ is a quasi-positive matrix describing population dispersal among patches in a heterogeneous environment and $Q$ is a diagonal matrix encoding within-patch population dynamics, the monotonicy of its spectral bound with respect to dispersal speed/coupling strength/travel frequency $\mu$ is established via two methods. The first method is an analytic derivation utilizing a graph-theoretic approach based on Kirchhoff's Matrix-Tree Theorem; the second method employs Collatz-Wielandt formula from matrix theory and complex analysis arguments. It turns out that our established result is a slightly strengthen version of Karlin-Altenberg's Theorem, which has previously been discovered independently while investigating reduction principle in evolution biology and evolution dispersal in patchy landscapes. Nevertheless, our result provides a new and effective approach in stability analysis of complex biological systems in a heterogeneous environment. We illustrate this by applying our result to well-known ecological models of single species, predator-prey and competition, and an epidemiological model of susceptible-infected-susceptible (SIS) type. This is joint work with Shanshan Chen, Junping Shi and Zhisheng Shuai.