首页 > 学术交流 > 学术活动 > 活动预告 > 正文

吴毅湘: Spectral Monotonicity of Perturbed Quasi-positive Matrices with Applications in Population Dynamics

分享到:
2020年01月07日 10:27 来源:数学与统计学院

报告承办单位:数学与统计学院

报告内容: Spectral Monotonicity of Perturbed Quasi-positive Matrices with Applications in Population Dynamics

报告人姓名:吴毅湘

报告人所在单位:美国中田纳西州立大学

报告人职称:助理教授,博士

报告时间2020年1月8日下午4:30

报告地点: 云塘校区理科楼A-419

报告人简介吴毅湘,博士,于2010年在中南大学获得理学学士学位,于2015年在美国路易斯安那大学获得理学博士学位。2015年7月至2016年8月在加拿大西安大略大学从事博士后研究。2016年9月至2019年7月,任美国范德堡大学助理教授(非终身制)。2019年8月,任美国中田纳西州立大学助理教授。目前,研究兴趣主要是反应扩散方程和生物数学。其研究成果已在《Nonlinearity》,《SIAM Appl Math》,《Bull Math Biology》,《J. Differential Equations》等国际数学杂志上发表论文10余篇。

报告摘要: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.

上一条:Jeong-Uk Kim: Analysis of Building Energy Demand under Standard Climate 下一条:张诚坚: Extended block boundary value methods for neutral equations with piecewise constant argument

关闭

友情链接