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 liapunov函数
 liapunov function
 In this article,we shall discuss a multimolecules reaction modelIf a=0,p=2, q≥2, by using the Hopf bifurcation theorem and liapunov function,we prove the existence,uniqueness,stability and asymptotic expressions of the Hopf bifurcation solution. 本文用Liapunov函数和Hopf分歧定理讨论一类多分子反应模型对a＝0，P＝2，q≥2，得到Hopf分歧解的存在性，唯一性，稳定性及分歧解的渐近表达式． 短句来源 After give the concept of the hyper-global asymptotic stability and weakly to get into monods μ(o) of Liapunov function v(t. X), disouss the hyper-global asymptotic stabality of nonautonomous system(1.1)and autonomous system(1.2). 在给出超全局渐近稳定和Liapunov函数V(t. X)弱进单子μ(o)的概念之后,讨论了非自治系统(1.1)和自治系统(1.2)的超全局浙近稳定。 短句来源 Solutions for a class of third order nonlinear differential equations are studied by using the Leray Schauder fixed point theorem and the method of Liapunov function. 运用 Leray－Schauder不动点定理和 Liapunov函数，研究了一类三阶非线性微分方程概周期解的存在性。 短句来源 (2)to study the stability of the nonlinear differen-tial systems with infinite delay by using the method of variation of constants, Liapunov function(need not find P-function)and the inequalities established; （2）结合常数变易法和Liapunov函数法（不必寻找P－函数），利用所建立的不等式研究了非线性无穷时滞微分系统的稳定性； 短句来源 The method is different from Liapunov function methods and approximate linear methods. 研究方法不同于有限维动力系统中通常使用的Liapunov函数方法与近似线性方法. 短句来源 更多
 liapunov functions
 In this paper,by establishing suitable Liapunov functions,we discussed the instability of solution for a class of the fourth order nonlinear and nonautonomous differential equation x ¨¨ +f(t,x,,,x…)+g(t,x,,)+h(t,x,)+p(t,x)=q(t,x,,,x…). :采用类比缓变系数的方法 ,作出了相应的Liapunov函数 ,研究了一类四阶非线性非自治微分方程x¨¨ + f(t,x , x ,¨x ,x…) + g(t,x , x ,¨x) +h(t ,x , x) + p(t,x) =q(t,x , x ,¨x ,x…)解的不稳定性 短句来源 In this paper, we give the definitions of (h0, h, M0)-global stability and (h0, h, M0)-boundedhess, and establish some crlterias for them by Liapunov functions. The results that we obtain supplement the results of [2] and generalize the corresponding results of [2] and [3]. 本文给出（h_0,h,M_0)—全局稳定性定义及（h_0,h,M_0)—有界性定义,并用Liapunov函数给出判别准则,所得结果补充了[1]且推广了[2]、[3]的相应结果。 短句来源 In this paper,we construct Liapunov functions of two nonlinear third order systems by the energy metric algorithm,then study their global asymptotic stability. 本文利用能量度量算法构造了两个三阶非线性系统的Liapunov函数 ,从而研究了它们零解的全局渐近稳定性 短句来源 Using the graph--theoretic decomposition method and the vector Liapunov function method, and constructing concrete Liapunov functions, in this paper, a criterion of globall stability was provided for some large-scale systems with general forms of z_i= g_l (t : Z_1. Z_2. …, Z_n (i=1. 2, …, n) The present results are much simple than those in which the graph- theoretic decomposition method is not used. 本文利用图论分解方法和向量Liapunov函数万法,通过具体地构造Liapunov函数给出具有形如: Z=g(t:Z_1,Z_2,…,Z_n)(i=1,2,…,n)的一般大系统全局渐近稳定的判定准则。 该准则与传统方法所得准则的适用范围互不包含。 短句来源 Liapunov Functions and Almost Periodic Solutions Liapunov函数与概周期解 短句来源 更多
 liapunov-function
 Through constructing Z-transform and Liapunov-function, a model of the spread of an epidemic is studied. Some sufficient conditions of a globally asymptotically stable solution of the model are obtained and a responsible explanation for real appearence on the spread of an epidemic is given. 通过构造Z变换和Liapunov函数 ,对一类传染病扩散模型进行了研究 ,得到了全局渐近稳定解的充分条件 ,进而对有关传染病扩散的实际现象给出了合理的解释 短句来源
 liapunov function method
 Using the graph--theoretic decomposition method and the vector Liapunov function method, and constructing concrete Liapunov functions, in this paper, a criterion of globall stability was provided for some large-scale systems with general forms of z_i= g_l (t : Z_1. Z_2. …, Z_n (i=1. 2, …, n) The present results are much simple than those in which the graph- theoretic decomposition method is not used. 本文利用图论分解方法和向量Liapunov函数万法,通过具体地构造Liapunov函数给出具有形如: Z=g(t:Z_1,Z_2,…,Z_n)(i=1,2,…,n)的一般大系统全局渐近稳定的判定准则。 该准则与传统方法所得准则的适用范围互不包含。 短句来源 The Present paper deals with the stability of a class delay differential equationsx ( t ) = -a(t)f (x(t-r(t)) +g( t, x(t) ) By using Liapunov function method, some stabitity criteria are obtained. 本文讨论了一类时滞微分方程 x(t)=-α(t)f(x(t-r(t)))+g(t,x(t))的稳定性,利用Liapunov函数法,得到了一组稳定性判据。 短句来源 The main issues are addressed as folllows: Firstly, using the Liapunov function method and the LaSalle invariance principle, some new sufficient conditions as well as the sufficient and necessary conditions of the boundedness and convergence of solutions are given. These results include and improve some important results associated with the same problems in the current literature. 主要工作是：第一，应用构造Liapunov函数以及Lasalle不变性原理，给出了解的有界性与收敛性的一些新的充分条件和充分必要条件，这些结果包含或扩展了已有文献关于同样问题的一些重要结果。 短句来源 Conditions of permanence for general discrete models with finite delays are established via the average Liapunov function method. The results are applied to both a 2 species delayed competition model (where the growth functions are exponential and rational respectively) and the n species Lotka Volterra model with delay. 以平均Liapunov函数方法为基础，对一般的有限时滞离散种群模型建立了一致持续生存条件．并将结果应用于一个增长函数分别为指数和分式形式的带时滞的两种群竞争模型，以及带时滞的n种群Lotka－Volterra模型 短句来源 The definition of partial synchronization under which the problem works is given. The stability of the method is analyzed by the Liapunov function method and the condition of choosing the control term is derived. 给出了此问题意义下的部分同步的定义,并以Liapunov函数方法分析了方法的稳定性,推导出了控制项的形式. 短句来源

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 liapunov function
 In this paper, global asymptotic stability for cellular neural networks with time delay is discussed using a novel Liapunov function. By introducing a Liapunov function and entropy, it is shown that the stability condition for the present system can be expressed as the principle of the extremum entropy production. Necessary and sufficient conditions for the existence of liapunov function of Lur'e form with Necessary and sufficient conditions are obtained for the existence of Liapunov function of Lur'e form with negative semi-definite derivative (i.e. The regression function and the Liapunov function are not zero at the sought-forx0; 2. 更多
 liapunov functions
 The Dulac's criterion is applied and liapunov functions are constructed to establish the global stability. Beyond any doubt, construction of Liapunov functions is an art. By combining the theory of exponential dichotomies with Liapunov functions, we obtain an intersting result on the existence of almost periodic solutions. Two families of liapunov functions for functional differential systems Two families of Liapunov functions are employed to study the global stability and boundedness of functional differential systems. 更多
 liapunov function method
 The analysis of disturbance rejection for singe-input singe-output (SISO) Lur'e system with norm uncertainty was concerned through invariant set analysis using Liapunov function method. The stability of the method is analyzed by the Liapunov function method and the condition of choosing the control term is derived. Because of the non-Markovian nature of the problem, we use the perturbed Stochastic Liapunov function method. Because of the non-Markovian nature of the problem, we use the perturbed Stochastic Liapunov function method, which is designed for such problems.
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