报告题目1：Equivariant Turing-Turing Bifurcations and Pattern Formation on a Square Domain

报告人：蒋卫华教授，哈尔滨工业大学

报告时间：2025年5月27日（周二）14:00-17:30

报告地点：20-200

报告摘要：In this talk, we present our recent work on equivariant Turing-Turing bifurcations and pattern formation in square spatial domains. For general reaction-diffusion systems with self-diffusion and cross-diffusion terms, we derive formulated results for the normal form and its coefficients on center manifolds near equivariant Turing-Turing singularities. Through analysis of the normal forms, we give approximate expressions for superposition-type steady states and their stability conditions in the original system. As an application, we analyze a plant-water interaction model to explore the formation of self-organized vegetation patterns in semi-arid regions.

报告人简介：蒋卫华，哈尔滨工业大学长聘教授，博士生导师。黑龙江省工业与应用数学学会常务理事，美国数学会《Math. Review》评论员。主要从事泛函微分方程和偏泛函微分方程的分支理论及应用的研究，在从高余维分支研究角度揭示复杂模式的存在性和稳定性方面有一些特色工作。主持和参与多项国家自然科学基金及省部级基金项目，研究工作主要发表在国内外诸如科学通报，JDE，JDDE，IMA J. Appl. Math.，DCDS A,B，SIADS，SAPM，JMB，JMAA，Nonlinear Anal，Nonlinear Anal. RWA，Physica D和JNS等重要学术期刊上，出版专著一部。

报告题目2：Global dynamics for a diffusive population model with distributed time delay

报告人：史峻平教授，美国College of William & Mary

报告时间：2025年5月27日（周二）14:00-17:30

报告地点：20-200

报告摘要：The global boundedness of solutions to a reaction-diffusion population model with memory-based movement governed by distributed time delays is proved. When the driving force of memory-based movement depending on the past-time distribution is controlled by a Gamma distribution function of order $k$, the scalar population equation is converted into a Keller-Segel type chemotaxis model with $k$ layers of indirect signals. Then the global boundedness of solution to the original system is proved through the one for the equivalent chemotaxis model with $k+1$ reaction-diffusion equations, and the global stability of the positive constant steady state is also shown by using the method of Lyapunov functionals. The results also improve some of the existing global boundedness of solutions to chemotaxis population model with indirect signals in the literature. This is a joint work with Xuanyu Lou, Chuncheng Wang and Dejun Fan.

报告人简介：史峻平，美国威廉玛丽学院(College of William & Mary)数学系教授，2018-2022年任数学系主任。1990-1993年南开大学学习，1998年毕业于美国杨百翰大学，获博士学位。主要研究方向为偏微分方程，动力系统，分歧理论，非线性泛函分析，生物数学。在偏微分方程，分歧理论方面的研究工作受到国际上广泛重视。在生物数学方向包括种群模型，生物化学反应，形态生成，生态系统稳定性等方面都有研究。主持参加美国国家科学基金会基金项目多项，主持组织国际学术会议20多次，在国际学术会议做大会报告/邀请报告100余次。担任多个国际知名SCI刊物编委，为100多种数学、物理、生物刊物审稿人。发表学术论文200余篇，被引用10000余次。

报告题目3：Exact multiplicity, bifurcation curves, and asymptotic profiles of endemic equilibria of a cross-diffusive epidemic model

报告人：吴毅湘教授，美国Middle Tennessee State University

报告时间：2025年5月27日（周二）14:00-17:30

报告地点：20-200

报告摘要：This study examines the global structure of endemic equilibrium (EE) solutions of a cross-diffusive epidemic model which incorporates the repulsive movement of the susceptible population away from the infected population. We show that the basic reproduction number $\mathcal{R}_0$ alone cannot determine the existence of the EEs and the model may have multiple EEs when the repulsive movement rate $\chi$ is large. We prove that the set of EEs forms a simple and unbounded curve bifurcating from the curve of disease free equilibria at $\mathcal{R}_0=1$ as $\mathcal{R}_0$ varies from zero to infinity, where the bifurcation curve can be forward or backward. We find conditions under which a forward bifurcation curve is of S-shaped and show that a large $\chi$ tends to induce backward bifurcation curves. Results on the asymptotic profiles of the EEs are obtained as the repulsive movement rate is large or the random movement rates are small. Finally, we perform numerical simulations to illustrate the results.

报告人简介：吴毅湘，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 (non-tenure track)。2019年8月，任美国中田纳西州立大学助理教授(tenure track)。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SIAM Journal on Mathematical Analysis、Nonlinearity、SIAM Journal on Applied Mathematics、Journal of Mathematical Biology、Journal of Differential Equations等国际数学杂志上发表论文40余篇。

报告题目4：Spatiotemporal dynamics of plankton driven by aquatic microorganisms

报告人：张继民教授，黑龙江大学

报告时间：2025年5月27日（周二）14:00-17:30

报告地点：20-200

报告摘要：Aquatic microorganisms are widely distributed in various aquatic environments. Bacteria, chytrids and lytic viruses are the three most important groups, and they have important implications for plankton spatiotemporal dynamics. Based on the existing ecological mechanisms and many ecological problems, we will propose phytoplankton-bacteria dynamics models, phytoplankton-zooplankton-chytrid dynamics models, phytoplankton-lytic virus dynamics models. Some critical thresholds are rigorously derived by analyzing dynamic properties of the models. Theoretical and numerical analysis revealed the influence mechanism of these three kinds of aquatic microorganisms on plankton.

报告人简介：张继民，黑龙江大学教授，博士生导师，九三学社社员，中国数学会生物数学专业委员会理事，黑龙江省数学会常务理事。2010年博士毕业于东北师范大学，2011年于吉林大学从事博士后研究工作，2016年和2019年访问美国威廉玛丽学院。主要从事微分方程，生物数学等方面的研究工作，主持国家自然科学基金，黑龙江省自然科学基金，中国博士后基金等项目10余项，发表学术论文50余篇。

邀请人：无限维动力系统和偏微分方程研究所