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。     

非线性时变系统的部分指数稳定性分析

讨论了非线性时变系统平凡解的部分指数稳定性和全局部分指数稳定性。分别利用数量与向量Lyapunov函数并结合数量与向量比较原理,得到了保证系统平凡解部分指数稳定和全局部分指数稳定的一系列充分条件。作为特殊情形,对于一类定常拟线性系统,在一定的条件下,若其对应的线性系统的平凡解是部分渐近稳定的,利用二次型Lyapunov函数得到了保证拟线性系统的平凡解是全局部分指数稳定的一个代数判据,这些结果在实际应用中具有一定的指导意义。最后用两个数值例子对所得主要结果加以阐明。     

Partial stability of a class of large-scale systems with partiallystable isolated subsystems

1.INTRODUCTION Partialstability(i.e.stabilitywithrespecttopartof thesystem’sstatevariables)playsanimportantrole instudyingofcontroltheoryanditsapplica tions[1～8],becausethestabilityofahigher order equationsisjustequivalenttothatofpartialstate variablesofacorrespondingsystemsoftheequations.Forsomeproblems,onemaybeinterestedonlyin somevariables,andinmethodologyitisverydifficult tosolveonceandforalltheproblemsabouthigher di mensionalsystems.Forexample,inmultispecies populationinteractionswh…     

Stability of Control Model of Investment

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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.     

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.     

Global stability for a heroin model with age-dependent susceptibility

This paper considers global asymptotic properties for an age-structured model of heroin use based on the principles of mathematical epidemiology where the incidence rate depends on the age of susceptible individuals. The basic reproduction number of the heroin spread is obtained. It completely determines the stability of equilibria. By using the direct Lyapunov method with Volterra type Lyapunov function, the authors show that the drug-free equilibrium is globally asymptotically stable if the basic reproduction number is less than one, and the unique drug spread equilibrium is globally asymptotically stable if the basic reproduction number is greater than one.     

基于Hopfield网络的不可分稳态大系统递阶优化控制

研究了整体目标函数关于各子系统具有不可加形式的大系统稳态优化控制问题 ,针对利用多目标优化技术把不可分问题转化为可分问题时采用的迭代策略使得计算较慢的问题 ,提出了具有递阶结构的基于 IPM的 Hopfield优化网络 ,并证明了该网络是渐进稳定的 ,其平衡点为原问题的最优点 .仿真表明 ,这是解决不可分稳态大系统优化问题的有效途径.     

一类非线性切换系统的稳定性分析

主要研究了一类非线性切换系统在某种切换律下的稳定性。证明了如果所有的子系统是线性时变的,并且在系统的Cauchy矩阵的范数满足某种条件的情况下,整个切换系统在任意切换律下是全局指数稳定的。研究了其带非线性扰动项的系统,在适当的假设下,建立了这种系统的全局稳定性特性。研究了某些子系统不满足上述Cauchy矩阵的范数条件的切换系统在某种切换律下的稳定性特性。     

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.     

Impulsive controller design for nonlinear networked control systems with time delay and packet dropouts

The globally exponential stability of nonlinear impulsive networked control systems(NINCS) with time delay and packet dropouts is investigated.By applying Lyapunov function theory,sufficient conditions on the global exponential stability are derived by introducing a comparison system and estimating the corresponding Cauchy matrix.An impulsive controller is explicitly designed to achieve exponential stability and ensure state converge with a given decay rate for the system.The Lorenz oscillator system is presented as a numerical example to illustrate the theoretical results and effectiveness of the proposed controller design procedure.     

具有时滞的二阶Hopfield神经网络的稳定性分析

对具有时滞的二阶Hopfield型神经网络平衡点的全局渐近稳定性问题进行了研究。在不要求连接权矩阵的对称性和输入输出函数的可微性与单调性的情况下 ,通过构造适当的Lyapunov泛函得到了网络平衡点的存在性和全局渐近稳定性的若干充分条件 ,这些条件可用于设计全局渐近稳定的二阶人工神经网络。     

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.     

Existence and Stability for Periodic Solution of Competition Reaction－Diffusion Models with Grazing Rates in Population Dynamics

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一类动力系统的时滞脉冲控制

针对脉冲控制中,时滞在脉冲采样时刻客观存在这样一种现象,研究了一类动力系统的时滞脉冲控制问题。给出了在时滞脉冲控制下,这类动力系统的原点是全局渐近稳定的一个充分条件,该条件反映了系统参数,脉冲区间和延迟时间之间的相关关系。利用所得的结论,也实现了这类系统的时滞脉冲同步。最后,以典型的分段线性系统Chua电路和非线性的混沌Chen系统为例,分别通过数值仿真实验验证了理论结论的有效性。     

Convergence and stability of the Newton-Like algorithm with estimation error in optimization flow control

The Newton-Like algorithm with price estimation error in optimization flow control in network is analyzed.The estimation error is treated as inexactness of the gradient and the inexact descent direction is analyzed.Based on the optimization theory,a sufficient condition for convergence of this algorithm with bounded price estimation error is obtained.Furthermore,even when this sufficient condition doesn't hold,this algorithm can also converge,provided a modified step size,and an attraction region is obtained.Based on Lasalle's invariance principle applied to a suitable Lyapunov function,the dynamic system described by this algorithm is proved to be global stability if the error is zero.And the Newton-Like algorithm with bounded price estimation error is also globally stable if the error satisfies the sufficient condition for convergence.All trajectories ultimately converge to the equilibrium point.     

基于IBM的递阶优化控制网络

研究了整体目标函数关于各子系统具有不可加形式的大系统稳态优化控制问题.针对利用多目标优化技术把不可分问题转化为可分问题时采用的选代策略使得计算较慢的问题,提出了具有递阶结构的基于IBM的Hopfield优化网络,并证明了该网络是渐进稳定的,其平衡点为原问题的最优点.仿真表明,这是解决不可分稳态大系统优化问题的有效途径.     

STABILITY OF N-DIMENSIONAL LINEAR SYSTEMS WITH MULTIPLE DELAYS AND APPLICATION TO SYNCHRONIZATION

This paper further investigates the stability of the n-dimensional linear systems with multiple delays. Using Laplace transform, we introduce a definition of characteristic equation for the n-dimensional linear systems with multiple delays. Moreover, one sufficient condition is attained for the Lyapunov globally asymptotical stability of the general multi-delay linear systems. In particular, our result shows that some uncommensurate linear delays systems have the similar stability criterion as that of the commensurate linear delays systems. This result also generalizes that of Chen and Moore （2002）. Finally, this theorem is applied to chaos synchronization of the multi-delay coupled Chua＇s systems.