报告题目1：Global Dynamics of Reaction-Diffusion Systems with a Time-varying Domain

报告人：赵晓强教授，加拿大纽芬兰纪念大学

报告时间：2025年10月23日（周四）8:30-9:10

报告地点：20-200

报告摘要：In this talk, I will report our recent research on the global dynamics of a large class of reaction-diffusion systems with a time-varying domain. By appealing to the theories  of asymptotically autononmous and periodic semiflows, we establish the threshold type results on the long-time behavior of solutions for such a system in the cases of  asymptotically bounded and periodic domains, respectively. To investigate the model system in the case of asymptotically unbounded domain, we first prove the global attractivity for nonautonomous reaction-diffusion systems with asymptotically vanishing diffusion coefficients via the method of sub- and super-solutions, and then use the comparison arguments to obtain the threshold dynamics. We also apply these analytical results to a reaction-diffusion model of Dengue fever transmission to study the effect of time-varying domain on the basic reproduction number.

报告人简介：赵晓强，加拿大纽芬兰纪念大学数学与统计系教授，该校University Research Professorship荣誉获得者。赵教授先后于1983年和1986年在西北大学数学系获学士和硕士学位，1990年在中国科学院应用数学研究所获博士学位。赵教授长期从事动力系统、微分方程和生物数学相关领域的研究，在单调动力学、一致持久性、行波解和渐近传播速度、主特征值、基本再生数的理论及应用等方面的系列工作受到同行的广泛关注和引用。迄今为止，他已在“Comm. Pure Appl. Math.、J. Eur. Math. Soc.、J. reine angew. Math.、J. Math. Pures Appl.、Trans. Amer. Math. Soc.、SIAM J. Math. Anal.” 等国际知名期刊上发表论文180余篇，并在Springer出版专著“Dynamical Systems  in Population Biology”。

报告题目2：Nonlocality-induced spatio-temproal dynamics in the memory-based diffusion equation

报告人：宋永利教授，杭州师范大学

报告时间：2025年10月23日（周四）9:10-9:50

报告地点：20-200

报告摘要：In this talk, the influence of the distributed delay (nonlocality in time) and nonlocal delay (nonlocality in space) on the stability and spatiotemporal dynamics in the memory-based diffusion populations are discussed. For the distributed delay, it has been shown that the weak kernel does not affect the stability of this positive constant steady state, but the strong kernel can lead to the rich dynamics. For the nonlocal delay, it has been shown that when movement driven by the memory-based diffusion is slow, the memory does not the  stability of positive homogeneous steady state, but when the movement driven by the memory-based diffusion is fast, the small memory delay (no matter how small it is) can destabilize the stability, however the large memory can stabilize the stability. A series of Turing bifurcation, Hopf bifurcation, Turing-Turing bifurcation and double Hopf bifurcation are explicitly determined.

报告人简介：宋永利，杭州师范大学数学学院教授、博士生导师、教育部新世纪优秀人才、浙江省高等学校“钱江学者”特聘教授、中国生物数学会理事。主要从事微分方程定性理论、无穷维动力系统的分支理论、斑图动力学的研究工作，取得了一系列高水平的研究成果，在动力系统领域的国际权威期刊SIAM J. Applied Dynamical Systems、SIAM J. Applied  Mathematics、 Journal of Differential Equations、  Journal of Nonlinear Science、Nonlinearity、Studies in Applied Mathematics、 IEEE Transactions on Neural Networks and Learning Systems、Physica D等发表学术论文90余篇。2014年起连续多年入选中国高被引学者榜单(数学类)。2022年入选斯坦福大学发布的全球前2%顶尖科学家榜单。曾主持多项国家自然科学基金和省部级重点项目的研究工作。2018年入选浙江省151人才工程第一层次培养人选、 2020年获“杭州市优秀教师”、“浙江省优秀数学教师”和“杭州师范大学优秀研究生导师”称号。研究成果获威海市科学技术一等奖和浙江省自然科学三等奖。

报告题目3：A periodic reaction-diffusion-advection SIS epidemic model with a saturated incidence function

报告人：崔仁浩教授，哈尔滨师范大学

报告时间：2025年10月23日（周四）10:00-10:40

报告地点：20-200

报告摘要：We are concerned with a reaction-diffusion-advection SIS (susceptible-infected-susceptible) epidemic model with a saturated incidence function in a spatio-temporally heterogeneous environment. We introduce the basic reproduction number R0 and establish the threshold dynamics for the disease transmission in terms of R0. The global attractivity of both the disease free and endemic periodic solution are shown in the special case of equal diffusion rates. More precisely, we explore the asymptotic properties of R0 with respect to the dispersal rates, the advection rate and the total population number. We further study the monotonicity and limiting profiles of R0 with respect to the period parameter. Moreover, we determine the spatial distribution of the disease when the diffusion rate of the infected population is sufficiently small. This work is joint with Dr. Xiaodan Chen and Prof. Xiao-Qiang Zhao.

报告人简介：崔仁浩，博士，教授，博士生导师；现为黑龙江省数学会常务理事，黑龙江省工业与应用数学会理事，国家自然科学基金数理学部通讯评议专家。主要研究方向为非线性泛函分析与偏微分方程，在JDE, CVPDE, SIAP等学术刊物上发表论文多篇；主持国家自然科学基金项目、全国博士后基金及黑龙江省自然科学基金等项目；作为主要完成人获得黑龙江省科学技术（自然科学）二等奖两项；2018年获黑龙江省数学会优秀青年学术奖；作为主持人获得黑龙江省高等教育教学成果二等奖一项。

报告题目4：Propagation direction of bistable pulsating waves for a nonlocal and delayed population model in discrete periodic habitat

报告人：余虓教授，华南师范大学

报告时间：2025年10月23日（周四）10:40-11:20

报告地点：20-200

报告摘要：How does spatio-temporal heterogeneity influence the propagation direction of bistable waves? To explore this question we formulate a nonlocal and time-delay population model with directional dispersal in discrete periodic habitat. Within a bistability framework, we determine the speed sign of bistable pulsating wave, followed by the existence and uniqueness of the pulsating wave. It turns out that time delay does not influence the sign but spatial heterogeneity does. Furthermore, an optimal dispersal strategy to maximize the speed is proved to exist.

报告人简介：余虓博士毕业于加拿大纽芬兰纪念大学，先后在美国迈阿密大学、加拿大瑞尔森大学和约克大学从事博士后研究。主要从事扩散系统的传播动力学研究，相关成果在JDE、JFA、JMPA、MA等杂志发表，主持国家自然科学基金青年和面上项目各1项。

邀请人：无穷维动力系统和偏微分方程研究所