中文色情

题    目：Diffusion contrast induced dynamics in a time-periodic competition-diffusion system with equal total resources

主讲人：王明新  教授

单    位：山西大学

时    间：9月14日  16:30

地    点：中文色情 南阶梯教室

摘    要：In this talk, we study a time-periodic, spatiotemporally heterogeneous competition- diffusion system, where two species have different intrinsic growth rates but equal total resources per period. Using asymptotic analysis and principal eigenvalue theory, we systematically examine its dynamics. When both diffusion rates are small, spatial heterogeneity of the difference in time-averaged resources leads to uniform persistence, stable coexistence, and asymptotic spatial segregation; whereas its spatial uniformity produces multiple regimes—fast-diffuser selection, parameter-dependent coexistence, or slow-diffuser dominance—separated by smooth threshold curves under different structural conditions. In the regime where at least one diffusion rate is large, we obtain a detailed classification of the local dynamics, with sharp delineation of parameter regions for stable coexistence, competitive exclusion, and a novel bistable scenario, where both semi-trivial periodic solutions are linearly stable while an unstable coexistence state also exists. We further characterize the asymptotic profiles of positive solutions in the mixed-scale diffusion limit. The results show that the interplay between temporal periodicity and spatial heterogeneity can overturn the classical "slower diffuser always prevails" principle, leading to a substantially richer range of ecological outcomes. This is a joint work with Dr. Zhenzhen Li at Central South University.

简    介：山西大学特聘教授。1994年起享受国务院政府特殊津贴，1998年任博士生导师，2007年起任二级教授。在J. Math. Pures Appl., Trans. Amer. Math. Soc., Proc. London Math. Soc., Indiana Univ. Math. J., Math. Models Meth. Appl. Sci., SIAM系列, J. Funct. Anal., CVPDE, JDE等国际知名期刊发表被SCI检索的论文280余篇。CRC出版社出版著作《Nonlinear Second Order Parabolic Equations》(独著)，Springer出版社出版合著《Nonlinear Second Order Elliptic Equations》(排名第一)，科学出版社出版著作5部(4部独著，1部合著)，高教出版社出版著作1部(独著)，清华大学出版社出版教材5部(3部独著，2部合著)。此外，还参与编写了由王元主编的《数学大辞典》。作为第一完成人，荣获教育部自然科学二等奖、江苏省科技进步二等奖、教育部科技进步三等奖各1项，还获得河南省青年科技奖、江苏省首届青年科学家奖提名奖、江苏省优秀研究生指导教师奖和华英文化教育基金奖。 1993年被授予河南省优秀专家称号。主持完成国家自然科学基金项目11项，在研一项；主持完成省部级项目8项。