威尼斯人

生物数学与网络动力学研讨会会议日程

报告摘要

Bifurcation analysis ofepidemic model on networks

靳祯  山西大学jinzhen@sxu.edu.cn

The bifurcation of most epidemic models on complexnetworks leading from a disease free equilibrium to an endemic equilibrium isforward. Gross et al. established a pair-approximation epidemic model for thespreading of infections on an adaptive network based on the well-known SISmodel, and numerical studies have figured out that the rewiring mechanism canlead to backward bifurcation and Hopf bifurcation. However,they have notpresented a strict mathematical proof of their conclusion in the literature. Inthis talk, we give the basic reproduction number and the critical conditions ofthe bifurcations occur analytically. Furthermore, we give a detailed analysisfor these rich dynamical behaviors, such as bistability and periodicity.

气候变暖和空间异质性对西尼罗河病毒扩散的影响

林支桂  扬州大学  zglin68@hotmail.com

我们用反应扩散方程组描述西尼罗河病毒的空间扩散，用自由边界表示病毒扩散的边沿。为了检查空间特征对病毒扩散的影响，我们定义了四个基本再生数，分别对应于常微分方程组问题、具齐次Neumann问题，齐次Dirichlet问题和自由边界问题。结果表明，在高风险区域，如果感染区域范围大或者扩散慢，病毒将蔓延；在低风险区域，小的初始感染病例，小的感染范围和大的扩散速率有利于病毒的消退。当病毒蔓延时我们证明了其空间扩散速度接近于一个常数。另外我们重点考察了全球气候变暖和空间异质性对西尼罗河病毒扩散的影响。

Bifurcationand pattern formation in a predator–prey model incorporating a prey refuge

王玮明  淮阴师范学院  weimingwang2004@163.com

In this talk, we will introduce ourrecent study on the spatiotemporal dynamics of a Leslie-Gower predator-preymodel incorporating a prey refuge subject to the Neumann boundary conditions.We mainly consider Hopf bifurcation and steady-state bifurcation whichbifurcate from the constant positive steady-state of the model.  In the case of Hopf bifurcation, by thecenter manifold theory and the normal form method, we establish the bifurcationdirection and stability of bifurcating periodic solutions; in the case ofsteady-state bifurcation, by the local and global bifurcation theory, we provethe existence of the steady-state bifurcation, and find that there are twotypical patterns, one is Turing bifurcation induced by diffusion, and the otheris spatiotemporal pattern induced by Turing-Hopf bifurcation. Via numericalsimulations, we find that the model exhibits not only stationary Turing patterninduced by diffusion which is dependent on space and independent of time, butalso temporal periodic pattern induced by Hopf bifurcation which is dependenton time and independent of space, and spatiotemporal pattern induced byTuring--Hopf bifurcation which is dependent on time and space. These resultsmay enrich the pattern formation in the predator-prey model.

EFFECTS OF ISOLATIONAND SLAUGHTER STRATEGIES IN

DIFFERENT SPECIES ONEMERGING ZOONOSES

崔景安  北京建筑大学  cuijingan@bucea.edu.cn

Zoonosis is the kind of infectiousdisease transmitting among different species by zoonotic pathogens. Differentspecies play different roles in zoonoses. Here, we established severalcross-species models to describe the zoonotic pathogen transmission fromwildlife, to domestic animals, to humans. Then we put three strategies into thebasic model to control the emerging zoonoses. Three strategies arecorresponding to control measures of isolation, slaughter or similar inwildlife, domestic animals and humans respectively. We analyzed the effects ofthese three strategies on control reproductive numbers and equilibriums and wetook avian influenza epidemic in China as an example to show the impacts of thestrategies on emerging zoonoses in different areas at beginning.

Bifurcations of aperiodically forced microbial continuous culture model with restrained growthrate

任景莉  郑州大学  ren_jingli@163.com

Athree dimensional microbial continuous culture model with a restrainedmicrobial growth rate is studied in this paper. Two types of dilution rates areconsidered to investigate the dynamic behaviors of the model. It is found thatperiodic perturbation can give rise to complex dynamics, such as quasiperiodicsolutions, periodic solutions of various periods, and chaos, which well explainoscillation phenomena in laboratory experiments.

动力学网络的类型转换与控制

傅新楚  上海大学  x.c.fu@163.com

我们生活在一个全面网络化的时代，网络已然成为复杂系统的一种基本结构形态。我们认识世界和改造世界的过程，就是和信息网络、社会网络、物联网络、生物网络等各种网络进行交互的过程。在复杂网络结构、行为研究和系统理解、构建与控制等方面，还存在哪些最有挑战性的问题，需要我们集智攻关？在复杂网络的基础理论、模型、方法和应用领域，通过这么多年的研究，还有什么关键点需要我们去突破？本报告讨论了若干网络动力学前沿问题，重点对下面的问题作了详细解读：一个复杂动态网络依其同步化区域为连通的无界区间、连通的有界区间、不连通的有界区间、不连通的无界区间（含两种情况）、或空集，分别称为类型I-类型VI。试讨论五个类型的动态网络通过施加适当的控制器从一个类型转换为另一个类型的问题。最好是在理论上得到较一般的结果，并对较特殊的网络得到理论和数值结果。这里的同步是指完全同步，控制可优先考虑牵制控制。

复杂系统结构建模与网络分析

唐旭清  江南大学  txq5139@jiangnan.edu.cn

主要介绍基于粒度的复杂系统最优层次结构建模方法与网络分析，及相关的应用研究，包括：最优层次结构建模；流感病毒蛋白的进化树构建；乳腺癌亚型异质性的分子标志探索与亚型识别等。

具有随机因素影响的神经网络模型的动力学分析

胡满峰  江南大学  humanfeng@jiangnan.edu.cn

随机现象随处可见，神经网络也不例外。报告内容围绕神经网络模型，介绍本人及学生的一些相关工作。

Signal Transmission ofBiological Reaction-Diffusion System by Using Synchronization

申建伟  许昌学院  xcjwshen@gmail.com

Molecularsignal transmission in cell is very crucial for information exchange. How tounderstand its transmission mechanism has attracted many researchers. In thispaper, we prove that signal transmission problem between neural tumor moleculesand drug molecules can be achieved by synchronous control. To achieve ourpurpose, we derive the Fokker-Plank equation by using the Langevin equation andtheory of random walk, this is a model which can express the concentrationchange of neural tumor molecules. Second, according to the biological characterthat vesicles in cell can be combined with cell membrane to release the cargowhich plays a role of signal transmission, we preliminarily analyzed the mechanismof tumor-drug molecular interaction. Third, we propose the view of synchronouscontrol which means the process of vesicle docking with their target membraneis a synchronization process, and we can achieve the precise treatment ofdisease by using synchronous control. We believe this synchronous controlmechanism is reasonable and two examples are given to illustrate thecorrectness of our results obtained in this paper.

Effectsof feedback regulation on vegetation patterns in semi-arid Environments

孙桂全  山西大学  sunguiquan@sxu.edu.cn

Itis well known that vegetation patterns characterize the distribution of thevegetation and provide some signs for vegetation protection. The positivefeedbacks regulation between the water and plant biomass play an important rolein the vegetation patterns in semi-arid environments, yet its influence onvegetation patterns is far from being well understood. In order to reveal amechanism of positive feedbacks on pattern formation, a water-biomass model insemi-arid environments with soil-water diffusion feedback is presented. Ourresults reveal that, as the soil-water diffusion intensity decreases, thepattern transitions: gap patterns → stripe (labyrinth) patterns → spot patternsemerge. More importantly, when the soil-water diffusion feedback intensity issmaller, the feedback will promote the growthof the vegetation; when thefeedback intensity is much larger, the vegetation biomass will decrease and thefeedback may induce the emergence of desertification. Additionally, therainfall can also induce the pattern transition. As the rainfall capacityincreases, the vegetation disappears and becomes the uniform vegetation state.Our findings highlight the relationship among feedback intensity, rainfall andpattern dynamics of the vegetation.

待定

刘玉荣    扬州大学   yrliu@yzu.edu.cn