微分方程及其应用学术研讨会

会议手册

 

河南·开封

2019年7月28-30日

 

微分方程及其应用学术研讨会

2019年7月28-30日

会议日程安排

7月29日（周一）上午
数学与统计学院学术报告厅
时间	报告人		题目
9:00-9:30	开幕式
	主持人：韩小森
	领导致词/照相
主持人：赵育林（中山大学）
9:30-10:15		李万同 （兰州大学）		Acceleration propagation for reaction-diffusion equations
10:15-10:35		茶歇
10:35-11:20		魏俊杰 （哈尔滨工业大学）		时滞-对流-反应扩散的单种群模型的Hopf分支分析
12:00午餐

7月29日（周一）下午
数学与统计学院学术报告厅
时间		报告人		题目
主持人：李万同（兰州大学）
14:30-15:15			袁荣 （北京师范大学）		Almost   periodic solutions and its module
15:15-16:35			茶歇
主持人：袁荣（北京师范大学）
16:35-16:20	赵育林 （中山大学）			二维雅可比猜想成立的条件
16:20-17:05	黄继才 （华中师范大学）			Bogdanov-Takens   bifurcation and its applications
18:30晚餐

 

7月30日（周二）上午
数学与统计学院学术报告厅
时间			报告人		题目
主持人：王智诚（兰州大学）
9:00-9:45				刘志华 （北京师范大学）	Bogdanov-Takens   bifurcation for age structured models
9:45-10:05				茶歇
主持人：刘志华（北京师范大学）
10:05-11:05	王智诚 （兰州大学）				Propagation dynamics of a time periodic and   delayed reaction-diffusion model without quasi-monotonicity
11:05-11:50	霍海峰 （兰州理工大学）				Modelling and analysis of a H1N1 model with relapse and effect   of Twitter
12：00午餐
7月30日（周二）下午
14:30-17:30		自由讨论

 

报告题目及摘要

报告人：黄继才（华中师范大学）

题  目：Bogdanov-Takens bifurcation and its applications

摘  要：In this talk, we firstly study the zeroes of Abelian integrals in unfoldings of codimension 3 singularities with nilpotent linear parts, which is the remaining problem in the study of degenerate Bogdanov-Takens bifurcation with codimension 3. Secondly, we will provide some applications of Bogdanov-Takens bifurcation in some biological and epidemiological models.

报告人：霍海峰 （兰州理工大学）

题  目：Modelling and analysis of a H1N1 model with relapse and effect of Twitter

摘  要：Twitter can play an important role in the control of influenza epidemics. We introduce a quantitative approach to evaluate the effects of Twitter on the spread of influenza epidemics in this talk. Statistically significant correlations between the number of the percentage of tweets that are self-reporting flu and the number of people with flu based on data of influenza-like illness reported cases and the percentage of tweets self-reporting flu during the 2009 H1N1 flu outbreak in England and Wales are shown from Pearson correlation and cross-correlation analyses. A new H1N1 model with relapse which involves impact of Twitter are also proposed. Stability of all the equilibria of our model are obtained. The occurrence of backward, forward and Hopf bifurcation are also established. The best-fit parameter values in our model are identified by grey wolf optimizer and nonlinear least square method from the above data. For determining key parameters during the outbreak of the disease with Twitter impact, the uncertainty and sensitivity analyses are explored by using a Latin hypercube sampling (LHS) method and evaluating the partial rank correlation coefficients (PRCCs). Our results show that Twitter reports have important implications for the control of infectious diseases and Twitter can serve as a good indicator of influenza epidemics.

报告人：李万同（兰州大学）

题  目：Acceleration propagation for reaction-diffusion equations

摘 要：In this talk, I will report the spatial propagation for reaction-diffusion cooperative systems. It is well-known that the solution of a reaction diffusion equation with monostable nonlinearity spreads at a finite speed when the initial condition decays to zero exponentially or faster, and propagates fast when the initial condition decays to zero more slowly than any exponentially decaying function. However, in reaction-diffusion cooperative systems, a new possibility happens in which one species propagates fast although its initial condition decays exponentially or faster. The fundamental reason is that the growth sources of one species come from the other species. Simply speaking, we find a new interesting phenomenon that the spatial propagation of one species is accelerated by the other species. This is a unique phenomenon in reaction-diffusion systems. We present a framework of fast propagation for reaction diffusion cooperative systems.

报告人：刘志华（北京师范大学）

题  目：Bogdanov-Takens bifurcation for age structured models

摘  要：The main purpose of this talk is to present our works recently on Bogdanov-Takens bifurcation in age structured models. We derive an easily feasible method for the determination of Bogdanov-Takens singularity in age structured models and show that some age structured models undergo the Bogdanov-Takens bifurcation. The analysis is based on the normal form theory and the center manifold theory for semilinear equations with non-dense domain combined with integrated semigroup theory.

报告人：王智诚（兰州大学）

题 目：Propagation dynamics of a time periodic and delayed reaction-diffusion model without quasi-monotonicity

摘  要：In this paper, we consider a time periodic non-monotone and nonlocal delayed reaction-diffusion population model with stage structure. We first prove the existence of the asymptotic speed $c^*$ of spread by virtue of two auxiliary equations and comparison arguments. By the method of super- and sub-solutions and the fixed point theorem, as applied to the truncated problem on a finite interval, and the limiting arguments, we then establish the existence of time periodic traveling wave solutions of the model system with wave speed $c>c^*$. We further use the results of the asymptotic speed of spread to obtain the nonexistence of traveling wave solutions for wave speed $c<c^*$. Finally, we prove the existence of the critical periodic traveling wave with wave speed $c=c^*$. It turns out that the asymptotic speed of spread coincides with the minimal wave speed for positive periodic traveling waves. These results are also applied to the model system with two prototypical birth functions.

报告人：魏俊杰（哈尔滨工业大学）

题  目：时滞-对流-反应扩散的单种群模型的Hopf分支分析

摘  要：本报告将介绍一类对流-时滞反应扩散的单种群模型的Hopf分支分析，包括非常值稳态解的存在性，Hopf分支的存在性，以及分支方向和分支周期解的稳定性的确定，并对时滞和空间非齐次性对模型的动力学性质的影响进行了分析。

报告人：袁荣（北京师范大学）

题  目：Almost periodic solutions and its module

摘  要：In this talk, I would like to introduce almost periodic functions, Stepanov’s almost periodic functions, piecewise continuous almost periodic functions, and its module. Some relationship and results will be shown.

报告人：赵育林（中山大学）

题  目：二维雅可比猜想成立的条件

摘  要：本文首先，通过Bendixson 紧致化理论得到二维雅可比猜想成立的新的充要条件。然后，利用新的充要条件，结合blow-up技巧给出若干个猜想成立的充分条件。