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.     

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.     

End-to-end rate-based congestion control with random loss: convergence and stability

The convergence and stability analysis for two end-to-end rate-based congestion control algorithms with unavoidable random loss in packets are presented, which can be caused by, for example, errors on wireless links. The convergence rates of these two algorithms are analyzed by linearizing them around their equilibrium points, since they are globally stable and can converge to their unique equilibrium points. Some sufficient conditions for local stability in the presence of round-trip delay are obtained based on the general Nyquist criterion of stability. The stability conditions can be considered to be more general. If random loss in the first congestion control algorithm is not considered, they reduce to the local stability conditions which have been obtained in some literatures. Furthermore, sufficient conditions for local stability of a new congestion control algorithm have also been obtained if random loss is not considered in the second congestion control algorithm.     

ON AN SIS EPIDEMIC MODEL WITH STAGE STRUCTURE

A SIS infectious disease model with stage structure consisting of immature and mature stages is proposed using a discrete time delay. The aim of the paper is to investigate under which conditions the disease becomes endemic or not and to find the difference between the model with stage structure and the corresponding model without stage structure. It is shown that either there exists a unique endemic equilibrium point which is globally asymptotically stable or the disease dies out by using an iterative scheme. The effect of the time delay on the populations at equilibria is considered.     

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.     

变时滞广义神经网络的指数稳定性

讨论具有可变时滞的Cohen Grossberg广义神经网络平衡态的稳定性问题。以推广的Halanay微分不等式为工具,通过构造合适的Lyapunov函数,结合Dini导数和不等式技巧,对具有可变时滞(适合于任何时滞有界情况)的广义神经网络平衡态的指数稳定性进行分析。在适当的假设条件下,得到了系统渐近指数稳定的几个充分性判据,与此同时也给出了相应的Lyapunov指数。     

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.     

时延高速通信网络的指数稳定跟踪控制

针对具有一个瓶颈和多用户的高速通信网络,当实际网络带宽的分配率跟踪上预定值,并且实际队列长度跟踪上给定的参考值,网络的数据丢失率就会很低,这时网络具有较高的利用率。本文基于线性矩阵不等式(LMI)和时延相关控制方法,设计一个控制器以实现指数稳定的跟踪控制。该控制器的设计只需知道时延的上界,指数稳定减少了过渡时间,加快了跟踪速度。当网络吞吐能力发生变化时,指数稳定使得新的平衡点很快达到,控制器无需调整参数,算法简单,易于实现。仿真实例说明了该控制器的有效性。     

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.     

具有时滞的区间大系统的鲁棒稳定性

应用Lyapunov函数方法讨论了具有时滞的区间大系统的鲁棒稳定性,给出了该系统鲁棒稳定的充分条件,同时还讨论了一类不确定时滞大系统的鲁棒稳定性,最后给出了结果的示例并与前人的结果进行了比较。     

Exponential stability for cellular neural networks: an LMI approach

A new sufficient conditions for the global exponential stability of the equilibrium point for delayed cellular neural networks （DCNNs） is presented. It is shown that the use of a more general type of Lyapunov-Krasovskii function enables the derivation of new results for an exponential stability of the equilibrium point for DCNNs. The results establish a relation between the delay time and the parameters of the network. The results are also compared with one of the most recent results derived in the literature.     

具有无界时变时滞的线性系统的稳定性

讨论了一类无界时变时滞线性系统的稳定性，给出了无界时变时滞线性系统稳定性的充分条件，这些条件也适用于常时滞系统。同时讨论了具有多个无界时变时滞系统的稳定性，并且改进了一些已有的关于常时滞系统稳定性的结论。最后给出了本文结论的两个示例。     

Study on Robust Uniform Asymptotical Stability for Uncertain Linear Impulsive Delay Systems

In the area of control theory the time-delay systems have been investigated. It's well known that delays often result in instability, therefore, stability analysis of time-delay systems is an important subject in control theory. As a result, many criteria for testing the stability of linear time-delay systems have been proposed. Significant progress has been made in the theory of impulsive systems and impulsive delay systems in recent years. However, the corresponding theory     

Delay-dependent exponential stability of impulsive stochastic systems with time-varying delay

The problem of delay-dependent exponential stability is investigated for impulsive stochastic systems with time-varying delay.Although the exponential stability of impulsive stochastic delay systems has been discussed by several authors,few works have been done on delay-dependent exponential stability of impulsive stochastic delay systems.Firstly,the Lyapunov-Krasovskii functional method combing the free-weighting matrix approach is applied to investigate this problem.Some delay-dependent mean square exponential stability criteria are derived in terms of linear matrix inequalities.In particular,the estimate of the exponential convergence rate is also provided,which depends on system parameters and impulsive effects.The obtained results show that the system will stable if the impulses’ frequency and amplitude are suitably related to the increase or decrease of the continuous flows,and impulses may be used as controllers to stabilize the underlying stochastic system.Numerical examples are given to show the effectiveness of the results.     

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.     

一类时滞动力网络的时滞相关稳定性

研究了节点含时滞的复杂动力网络在平衡点的稳定性.基于时滞微分不等式和李雅普诺夫稳定性理论,提出了此网络的时滞相关的局部渐近稳定的充分条件,并给出了时滞上界的具体表达式.最后的数值模拟分析表明结果是可行且有效的.     

Robust stability analysis of uncertain discrete-time systems with state delay

The sufficient conditions of stability for uncertain discrete-time systems with state delay have been proposed by some researchers in the past few years, yet these results may be conservative in application. The stability analysis of these systems is discussed, and the necessary and sufficient condition of stability is derived by method other than constructing Lyapunov function and solving Riccati inequality. The root locations of system characteristic polynomial, which is obtained by augmentation approach and Laplace expansion, determine the stability of uncertain discrete-time systems with state delay, the system is stable if and only if all roots lie within the unit circle. In order to analyze robust stability of system characteristic polynomial effectively, Kharitonov theorem and edge theorem are applied. Example shows the practicability of these methods.     

延迟多重休假MX/G/1排队系统的队长分布

考虑延迟多重休假的M^x／G／1排队，在假定延迟时间、休假时间和服务时间都是一般概率分布函数下，研究了队长的瞬态和稳态性质、通过引进“服务员忙期”，导出了在任意时刻t瞬态队长分布的L变换的递推表达式和稳态队长分布的递推表达式，以及平稳队长的随机分解．     

Stability Analysis and Performance Evaluation of Delayed Bilateral Telerobotic Systems over a Lossy Communication Channel

The focus of this paper is to address a novel control technique for stability and transparency analysis of bilateral telerobotic systems in the presence of data loss and time delay in the communication channel. Different control strategies have been reported to compensate the effects of time delay in the communication channel;however, most of them result in poor performance under data loss. First, a model for data loss is proposed using a finite series representation of a set of periodic continuous pulses.To improve the performance and data reconstruction, a holder circuits is also introduced. The passivity of the overall system is provided via the wave variable technique based on the proposed model for the data loss. The stability analysis of the system is then derived using the Lyapunov theorem under the time delay and the data loss. Finally, experimental results are given to illustrate the capability of the proposed control technique.     

Existence and Stability of Positive PeriodicSolution of Delay Logistic Ecosystem with Feedback Control and Diffusion

1IntroductionWeconsiderthedelaylogisticecosystemwithfeedbackcontrolanddiffusionoftheformConcerningthestabilityproblemofpositivestead-stateforsystem(1.1),ithasbeendiscussedbyX.Shengli[1],whereastheasymptoticbehaviorofsolutionsofsystem(1.1)withoutdiffusionhasalsobeenconsideredbyK.Gopalsamy[2]andtheoscillationofsystem(1.1)withoutdiffusionandfeedbackcontrolcanbefoundinreference[3](K.GopalsamyandG.Ladas),Inreference[4],J.Dangpinghasgivedsufficientconditionsofexistenceandstabilityofperiodicsolut…