为促进国内动力系统与生物数学的发展，加强本领域的学术交流与合作，将于2022年9月16日在线上腾讯会议举办“动力系统与生物数学研讨会”。会议由中国科学院数学与系统科学研究院动力系统研究中心主办。

 

会议日程

2022年9月16日 星期五

会议秘书：郭松柏，中国科学院数学与系统科学研究院&北京建筑大学（电话：18801179538 邮箱：sonbguo@amss.ac.cn）

报告信息

On the stochastic stability of limiting measures in SODEs

蒋继发  上海师范大学

Abstract: We exploit limiting measures of stationary measures of stochastic ordinary differential equations. Such measures are more stable than other invariant measures of unperturbed systems or the most stable if they uniquely exist to stochastic perturbations. Using the Freidlin-Wentzell large deviations principle, we prove that limiting measures are concentrated away from repellers which are topologically transitive, or equivalent classes, or admit Lebesgue measure zero. We also preclude concentrations of limiting measures on acyclic saddle or trap chains and prove that limiting measures are concentrated on minimal elements of the partial order induced by the Freidlin-Wentzell’s equivalent relation, which are Liapunov stable if there are a finite number of equivalent classes. Applications are made to the Morse-Smale systems, the Axiom A systems including structural stability systems and separated start systems, the gradient or gradient-like systems, those systems possessing the Poincaré-Bendixson property with a finite number of limit sets to obtain that limiting measures live on Liapunov stable critical elements, Liapunov stable basic sets, Liapunov stable equilibria, Liapunov stable limit sets including saddle or trap cycles, respectively. A number of nontrivial examples admitting a unique limiting measure are provided, which include monostable and multistable systems. This is a joint work with Xu Tianyuan and Chen Lifeng.

异质性传染病动力学模型与应用

崔景安  北京建筑大学

摘要：传染病的传播与控制过程中，基本再生数、最终规模、免疫策略问题的研究至关重要. 针对异质的多种群传染病模型探讨了基本再生数与最终规模的关系，应用于一些传染病案例与免疫策略的研究.

Invariant manifolds with/without spectral gap

张伟年  四川大学

Abstract: In this talk we discuss invariant manifolds obtained with or without a spectral gap condition, showing approximation to weak hyperbolic manifolds (with gap condition) and giving the existence and smoothness for invariant submanifolds on a center manifold (without gap condition).

Averaging principle for monotone SPDEs

柳振鑫 大连理工大学

Abstract: The first Bogolyubov theorem on averaging for SDEs has been investigated extensively. In this talk, we will discuss the second Bogolyubov theorem and global averaging principle for monotone SPDEs. This talk is based on our joint work with Mengyu Cheng.

Multiscale dynamic models for disease transmission dynamics

肖燕妮  西安交通大学

Abstract: Coupling the models in different scales becomes challenging. In this talk I shall briefly give an introduction to modelling approach at both population and individual level. I shall give an idea of developing a multi-scale model that nests the within-host dynamics into the between-host by linking the transmission rate and the disease-induced death rate to viral loads within infected individuals. I take HIV transmission dynamics as an example to illustrate and examine the impact of ART on individual level on HIV new infections on population, to investigate the optimal control on different scales. I then present our recent work on COVID-19 infection, including a stochastic individual based model on complex networks with four layers, to interpret why children play a different role in the four epidemic waves of COVID-19 pandemic. Finally, I shall give concluding remarks on multi-scale modelling approach.

具有非线性感染率、反馈控制和时滞的SI传染病模型的全局稳定性

马万彪  北京科技大学

摘要：我们考虑一类具有饱和型功能反应函数、2个反馈控制与多个时滞的SI传染病模型,通过构造适当的Lyapunov泛函, 并结合Lyapunov-LaSalle不变性原理, 建立了该模型的平衡态全局稳定的充分条件.