THE GLOBAL STABILITY OF A COMPETINGCHEMOSTAT MODEL WITH DELAYED NUTRIENT RECYCLING

In this paper, by applying the method of Liapunov functionals we study the global stability of the positive equilibrium of a competing chemostat model with delayed nutrient recycling. The sufficient conditions of the global stability (involved in average time delay or not) are obtained.     

STUDY ON AN SIS EPIDEMIC MODEL WITH TIME VARIANT DELAY

In this paper, we study an SIS epidemic model with a time variant delay. By means of Liapunov functional, some sufficient conditions of global stability to endemic equilibrium and disease free equilibrium have been obtained. The influence of time delay on the stability of equilibria is displayed.     

Research on Rumor Spreading Model with Time Delay and Control Effect

Information flow retains a critical role in decision making among investors. In this paper,we employ a diffusion model based on epidemiology theory to study the rumor spreading process within investors. The paper introduce the feedback mechanism of classical control theory into the model, which helps to reflect the interaction between rumor spreaders and information supervision.Further we apply a time delay factor to give investors access to transparent information and change their behavior. Subsequently, the stability of the rumor disappearance equilibrium and the rumor existence equilibrium are analyzed and the condition for the system undergoes a Hopf-bifurcation is given. The mathematical arguments are subjected to numerical simulations to present the ideal case scenarios. The results suggest that, increase the general strength of information supervision and the proportion coefficient associated with the infected population in the short-term delay are conducive to better control.     

Global Attractiveness in a Predator-Prey System with Stage Structure

In this paper, we establish a mathematical model of two species with stage structure and the relation of predator-prey, to obtain conditions that determine the stability of the populations. By the application of comparing argument and exploiting the monotonicity of one equation of the model, we obtain sufficient conditions for the global attractiveness of positive equilibrium .     

Global Stability in a Competition Model of Plankton Allelopathy with Infinite Delay

A competition model of plankton allelopathy with infinite delay is considered in this paper.By using an iterative method, the global stability of the interior equilibrium point of the system is investigated. The result shows that for this system, delay and toxic substances are harmless for the stability of the interior equilibrium point.     

受有毒物质影响的广义生物系统的变结构控制

根据营养动力学和生态毒理学原理建立了一个受环境中有毒物质影响的广义生物系统模型,基于模型非负平衡点的生物含义,提出了一个既使环境中有毒物质浓度降低到不危害模型中种群生存的程度,又使种群在其最大密度值附近持续生存的理想平衡点,根据变结构控制原理,设计控制器使模型在短时间内跟踪且稳定于该平衡点,最后,通过数值模拟验证模型的有效性.     

A singular bioeconomic model with diffusion and time delay

This paper studies a prey-predator singular bioeconomic system with time delay and diffusion, which is described by differential-algebraic equations. For this system without diffusion, there exist three bifurcation phenomena: Transcritical bifurcation, singularity induced bifurcation, and Hopf bifurcation. Compared with other biological systems described by differential equations, singularity induced bifurcation only occurs in singular system and usually links with the expansion of population. When the diffusion is present, it is shown that the positive equilibrium point loses its stability at some critical values of diffusion rate and periodic oscillations occur due to the increase of time delay. Furthermore, numerical simulations illustrate the effectiveness of results and the related biological implications are discussed.     

GLOBAL STABILITY AND HOPF BIFURCATION OF AN SIS EPIDEMIC MODEL WITH TIME DELAYS

1 IntroductionFor epidemic model with delays, many people have done a lot of work and many valuableresults have been obtained. In SIS ePidemiologic models, susceptibles become infectious aftersufficieot contact with an infective and then become susceptible again after they have recoveredfrom the infection. SIS models with a time delay in the infectious class and a constan poWulation size were analyzed by Cooke and Yorke[1] and Greenberg and Hoppensteadt[2J. TheyfOund that aJl solutions a…     

反沉默螺旋效应下社交媒体谣言传播动力学研究

目前，社交媒体已经成为网络谣言滋生的温床，其庞大的用户规模，以及即时性、开放性等特点，使得谣言传播的广度和速度远远高于现实社会网络，从而对人们的生活和社会的稳定产生巨大的影响.为此，基于传染病动力学及"反沉默螺旋"理论，构建了考虑辟谣行为及网络结构的社交媒体谣言传播模型；并进一步分析了模型中无谣言平衡点和谣言存在平衡点的存在性和稳定性，计算了模型的基本再生数；利用MATLAB对模型中各参数变化对谣言传播的影响进行了仿真分析，并对部分参数进行了敏感性分析；利用实际案例对模型进行了进一步的分析与验证；最后，给出了控制社交媒体中谣言传播的策略建议.     

连续型联想细胞神经网络局部指数稳定性研究

由于细胞神经网络的潜在应用前景 ,它现已成为神经网络研究的新热点。首先给出连续型联想细胞神经网络的数学模型 ,得到了连续型细胞神经网络平衡点局部指数稳定的充要条件及平衡点指数吸引域的估计 ,研究表明对平衡点的指数吸引域的估计 ,只要计算平衡点处的导算子矩阵的对数范数即可。该研究对连续型联想细胞神经网络的设计和应用均有重要的作用。     

异性人口的HIV/AIDS流行病模型的分岔

在异性人口中HIV的传播对HIV／AIDS流行病产生了极大的影响，这一事实早已被人们所认识。本文通过异性人口的HIV／AIDS流行病的非对称模型的分岔问题的讨论，给出了这个模型的实际定义与解释，并运用中心流行定理及其计算方法得到，在这个模型的疾病消除平衡点处出现静态分岔，且它的分岔的余维数等于一。由此得到这个系统是结构不稳定的，因此社会环境的改变对疾病控制也起着重要作用。     

几类传染病模型中基本再生数的计算

通过参考大量文献,系统整理了几类经典的传染病模型,并对传染病模型基本再生数的几种导出方法做了一个综述。文中综合了传染病动力学模型的分析方法和复杂网络理论,分别从基本再生数的定义,初始时刻染病者的单调性,正平衡点的存在性,无病平衡点的局部稳定性,即通过计算基本再生矩阵或者雅克比矩阵的特征值,数值模拟,这几个角度给出了基本再生数的导出方法,并举例说明了几类主要的传染病模型,特别是网络传播模型中基本再生数的计算方法,给出了基本再生数的特点,并对基本再生数时变的情况进行了具体分析。     

学习效应、有限理性与动态古诺竞争复杂性

引入"学习效应"的思想,构建了一类具有学习效应的有限理性古诺竞争模型,利用非线性动力系统的分支理论研究了该模型均衡点的存在性与稳定性,并进行了对比研究与数值仿真。研究结果表明学习效应对动态古诺竞争复杂性有显著影响:系统稳定域随着企业学习效应的增强而增大;系统到达均衡的速度随着企业学习效应的增强而加快;企业产量调整速度的变化对模型的稳定性有较明显的影响。     

中期经济增长和结构变化——递推动态一般均衡分析

预测了中国未来１５年的经济增长和结构变化．基于对未来人口、劳动力的增长和部门水平上的技术变化的估计,本文运用递推动态的多部门可计算一般均衡（ＣＧＥ）模型,模拟了１９９５年～２０１０年中国经济增长和产业、就业和贸易结构的变化趋势．本文强调了非中性的技术变化对于经济增长和结构变化的重要作用     

人口模型中的分岔现象

在非线性动态系统中可能出现分岔现象,分岔理论为我们研究社会经济系统中的某些异常现象提供了一种新方法。本文研究了人口模型的分岔现象,以此作为示例,体现了用分岔理论研究社会经济系统的过程与步骤。     

捕食者具有传染病的时滞捕食系统模型分析

提出了一类捕食者具有传染病的时滞生态-流行病模型.该模型中,捕食者和食饵均具有密度制约,并引入时滞对模型加以讨论.利用特征根法、函数分析法及线性化方法对模型动力学特性进行分析.证明了模型平衡点的存在性并分析其渐近稳定性,得出系统平衡点的渐近稳定性和Hopf分支存在的充分条件.     

合作竞争博弈中的复杂性与演化均衡的稳定性分析

从博弈参与人的有限理性出发,探讨了合作竞争博弈中复杂性存在的根源,在此基础上应用演化博弈论的方法探讨了合作竞争博弈的演化模型,这是一个复制动态模型,因而我们可以借用生物学中的"复制动态"机制来模拟参与人的学习与调整机制,用"进化稳定策略"来描述合作竞争博弈的长期演化趋势,最后分析了一个水平差异化产品的合作竞争博弈的演化均衡与稳定性,及其演化过程中所表现出来的复杂性.     

具有惩罚策略的公共物品博弈与合作演化

采用演化博弈方法,研究具有代价的第二方惩罚机制对于公共物品博弈均衡选择及群体合作行为的影响.将群体策略选择过程描述成一个多维马氏过程,通过极限分布分析系统演化稳定状态.分别考虑只对背叛策略进行惩罚的一阶惩罚机制和同时对背叛及不惩罚背叛的合作(二阶背叛)都进行惩罚的二阶惩罚机制.研究发现,与一阶惩罚相比,二阶惩罚机制可以在更大参数范围内促进群体合作的产生,系统存在选择不同均衡结果的惩罚参数临界值.并将结果与复制动态模型进行了对比.     

Global Dynamics for an HIV Infection Model with Crowley-Martin Functional Response and Two Distributed Delays

In this paper, an HIV dynamics model with two distributed intracellular delays incorporating Crowley-Martin functional response infection rate is investigated. The authors take into account multiple stage disease transmission and the latently infected cells (not yet producing virus) in our system. The authors consider nonnegativity, boundedness of solutions, and global asymptotic stability of the system. By constructing suitable Lyapunov functionals and using the Lyapunov-LaSalle invariance principle, the authors prove the global stability of the infected (endemic) equilibrium and the diseasefree equilibrium for time delays. The authors have proven that if the basic reproduction number R₀ is less than unity, then the disease-free equilibrium is globally asymptotically stable, and if R₀ is greater than unity, then the infected equilibrium is globally asymptotically stable. The results obtained show that the global dynamic behaviors of the model are completely determined by the basic reproduction number R₀ and that the time delay does not affect the global asymptotic properties of the model.     

不同理性预期下Stackelberg模型的动态复杂性

构建双寡头参与人分别采取有限理性和天真理性预期的Stackelberg博弈模型,研究市场均衡的稳定性条件及动态复杂性特征.通过理论求解和数值模拟得出结论:参与人在不完全信息和不同理性情况下,Stackelberg模型的参数取值范围决定了动态系统的稳定性、产量分岔、利润分岔、奇怪吸引子、吸引子维数和混沌等;如果参数取值满足一定条件,静态Stackelberg推测变差均衡能够实现;否则,Stackelberg推测变差均衡不稳定,非线性动态经济系统可能会出现周期变化或混沌的现象.