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BOUNDEDNESS AND PERSISTENCE AND GLOBAL ASYMPTOTIC STABILITY FOR A CLASS OF DELAY DIFFERENCE EQUATIONS WITH HIGHER ORDER
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作者 李先义 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2002年第11期1331-1338,共8页
Some sufficient, conditions for boundedness and persistence and global asymptotic stability of solutions for a class of delay difference equations with higher order are obtained, which partly solve G. Ladas' two o... Some sufficient, conditions for boundedness and persistence and global asymptotic stability of solutions for a class of delay difference equations with higher order are obtained, which partly solve G. Ladas' two open problems and extend some known results. 展开更多
关键词 delay difference equation boundedness and persistence global asymptotic stability open problem
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DISCUSSION ON″THE BOUNDEDNESS AND ASYMPTOTIC BEHAVIOR OR SOLUTION DIFFERENTIAL SYSTEM OF SECOND-ORDER WITH VARIABLE COEFFICIENT" (App1ied Mathematics and Mechanics,Vo1.3,No.4,1982)
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作者 毛士忠 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1984年第3期1419-1423,共5页
After reading the article "The Boundedness and Asymptotic Behavior of Solution of Differential System of Second-Order with Variable Coefficient" in "Applied Mathematics and Mechanics", Vol. 3, No. ... After reading the article "The Boundedness and Asymptotic Behavior of Solution of Differential System of Second-Order with Variable Coefficient" in "Applied Mathematics and Mechanics", Vol. 3, No. 4, 1982, we would like to put forward a few points to discuss with the author and the readers. Our opinions are presented as follows: 展开更多
关键词 DISCUSSION ON THE boundedness AND asymptotic BEHAVIOR OR SOLUTION DIFFERENTIAL SYSTEM OF SECOND-ORDER WITH VARIABLE COEFFICIENT App1ied Mathematics and Mechanics Vo1.3 No.4 1982
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ON THE ASYMPTOTIC BEHAVIOR OF HOLOMORPHIC ISOMETRIES OF THE POINCAR DISK INTO BOUNDED SYMMETRIC DOMAINS 被引量:1
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作者 Ngaiming Mok 《Acta Mathematica Scientia》 SCIE CSCD 2009年第4期881-902,共22页
In this article we bounded symmetric domains study holomorphic isometries of the Poincare disk into Earlier we solved the problem of analytic continuation of germs of holomorphic maps between bounded domains which a... In this article we bounded symmetric domains study holomorphic isometries of the Poincare disk into Earlier we solved the problem of analytic continuation of germs of holomorphic maps between bounded domains which are isometrics up to normalizing constants with respect to the Bergman metric, showing in particular that the graph 170 of any germ of holomorphic isometry of the Poincar6 disk A into an irreducible bounded symmetric domain Ω belong to C^N in its Harish-Chandra realization must extend to an affinealgebraic subvariety V belong to C × C^N = C^N+1, and that the irreducible component of V ∩ (△ × Ω) containing V0 is the graph of a proper holomorphic isometric embedding F : A→ Ω. In this article we study holomorphie isometric embeddings which are asymptotically geodesic at a general boundary point b ∈ δ△. Starting with the structural equation for holomorphic isometrics arising from the Gauss equation, we obtain by covariant differentiation an identity relating certain holomorphic bisectional curvatures to the boundary behavior of the second fundamental form σ of the holomorphie isometric embedding. Using the nonpositivity of holomorphic bisectional curvatures on a bounded symmetric domain, we prove that ‖σ‖ must vanish at a general boundary point either to the order 1 or to the order 1/2, called a holomorphie isometry of the first resp. second kind. We deal with special cases of non-standard holomorphic isometric embeddings of such maps, showing that they must be asymptotically totally geodesic at a general boundary point and in fact of the first kind whenever the target domain is a Cartesian product of complex unit balls. We also study the boundary behavior of an example of holomorphic isometric embedding from the Poincare disk into a Siegel upper half-plane by an explicit determination of the boundary behavior of holomorphic sectional curvatures in the directions tangent to the embedded Poincare disk, showing that the map is indeed asymptotically totally geodesic at a general boundary point and of the first kind. For the metric computation we make use of formulas for symplectic geometry on Siegel upper half-planes. 展开更多
关键词 holomorphic isometry Bergman metric Poincar DISK analytic continuation bounded symmetric domain asymptotic geodesy second fundamentalform Siegel upper half-plane symplectic geometry
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Asymptotic bounded consensus tracking of double-integrator multi-agent systems with bounded-jerk target based on sampled-data without velocity measurements
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作者 Shuang-Shuang Wu Zhi-Hai Wu +1 位作者 Li Peng Lin-Bo Xie 《Chinese Physics B》 SCIE EI CAS CSCD 2017年第1期591-596,共6页
This paper investigates asymptotic bounded consensus tracking(ABCT) of double-integrator multi-agent systems(MASs) with an asymptotically-unbounded-acceleration and bounded-jerk target(AUABJT) available to parti... This paper investigates asymptotic bounded consensus tracking(ABCT) of double-integrator multi-agent systems(MASs) with an asymptotically-unbounded-acceleration and bounded-jerk target(AUABJT) available to partial agents based on sampled-data without velocity measurements. A sampled-data consensus tracking protocol(CTP) without velocity measurements is proposed to guarantee that double-integrator MASs track an AUABJT available to only partial agents.The eigenvalue analysis method together with the augmented matrix method is used to obtain the necessary and sufficient conditions for ABCT. A numerical example is provided to illustrate the effectiveness of theoretical results. 展开更多
关键词 asymptotic bounded consensus tracking multi-agent systems without velocity measurements sampled-data control
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Asymptotic Behavior of a Stochastic SIRS Model with Non-linear Incidence and Levy Jumps 被引量:2
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作者 臧彦超 李俊平 《Journal of Donghua University(English Edition)》 EI CAS 2014年第3期217-223,共7页
A stochastic susceptible-infective-recovered-susceptible( SIRS) model with non-linear incidence and Levy jumps was considered. Under certain conditions, the SIRS had a global positive solution. The stochastically ulti... A stochastic susceptible-infective-recovered-susceptible( SIRS) model with non-linear incidence and Levy jumps was considered. Under certain conditions, the SIRS had a global positive solution. The stochastically ultimate boundedness of the solution of the model was obtained by using the method of Lyapunov function and the generalized Ito's formula. At last,asymptotic behaviors of the solution were discussed according to the value of R0. If R0< 1,the solution of the model oscillates around a steady state, which is the diseases free equilibrium of the corresponding deterministic model,and if R0> 1,it fluctuates around the endemic equilibrium of the deterministic model. 展开更多
关键词 susceptible-infective-recovered-susceptible(SIRS) epidemic model Levy noise stochastic ultimate boundedness asymptotic behavior
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On the Asymptotic Behavior of Certain Second Order Differential Equations 被引量:3
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作者 XUZhi-ting XIAYong 《Chinese Quarterly Journal of Mathematics》 CSCD 2004年第2期186-187,共2页
Two criteria for asymptotic behavior of certain second order differential equations are obtained. The results extend and improve Feng's theorem.
关键词 asymptotic behavior second order differential equation bounded
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On the Stability and Boundedness of Solutions of Certain Non-Autonomous Delay Differential Equation of Third Order 被引量:2
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作者 Akinwale L. Olutimo Daniel O. Adams 《Applied Mathematics》 2016年第6期457-467,共11页
In this paper, we study certain non-autonomous third order delay differential equations with continuous deviating argument and established sufficient conditions for the stability and boundedness of solutions of the eq... In this paper, we study certain non-autonomous third order delay differential equations with continuous deviating argument and established sufficient conditions for the stability and boundedness of solutions of the equations. The conditions stated complement previously known results. Example is also given to illustrate the correctness and significance of the result obtained. 展开更多
关键词 asymptotic Stability boundedness Lyapunov Functional Delay Differential Equations Third-Order Delay Differential Equations
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ON THE ASYMPTOTIC BEHAVIOUR OF SOLUTIONS OF CERTAIN FIFTH-ORDER ORDINARY DIFFERENTIAL EQUATIONS
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作者 Cemil Tunc 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2003年第8期893-901,共9页
The sufficient conditions are given for all solutions of certain non- autonomous differential equation to be uniformly bounded and convergence to zero as t →∞ ?. The result given includes and improves that result ob... The sufficient conditions are given for all solutions of certain non- autonomous differential equation to be uniformly bounded and convergence to zero as t →∞ ?. The result given includes and improves that result obtained by Abou-El-Ela & Sadek . 展开更多
关键词 asymptotic behaviour boundedness CONVERGENCE
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Asymptotical mean square stability of cellular neural networks with random delay
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作者 朱恩文 王勇 +1 位作者 张汉君 邹捷中 《Journal of Harbin Institute of Technology(New Series)》 EI CAS 2010年第3期409-413,共5页
In this paper,the asymptotical mean-square stability analysis problem is considered for a class of cellular neural networks (CNNs) with random delay. Compared with the previous work,the delay is modeled by a continuou... In this paper,the asymptotical mean-square stability analysis problem is considered for a class of cellular neural networks (CNNs) with random delay. Compared with the previous work,the delay is modeled by a continuous-time homogeneous Markov process with a finite number of states. The main purpose of this paper is to establish easily verifiable conditions under which the random delayed cellular neural network is asymptotic mean-square stability. By using some stochastic analysis techniques and Lyapunov-Krasovskii functional,some conditions are derived to ensure that the cellular neural networks with random delay is asymptotical mean-square stability. A numerical example is exploited to show the vadlidness of the established results. 展开更多
关键词 cellular neural networks asymptotical mean-square stability random delay linear matrix inequality
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Stability and Boundedness of Solutions of Certain Non-Autonomous Third Order Nonlinear Differential Equations
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作者 Akinwale L. Olutimo Folashade O. Akinwole 《Journal of Applied Mathematics and Physics》 2016年第1期149-155,共7页
In this paper, by defining an appropriate Lyapunov functional, we obtain sufficient conditions for which all solutions of certain real non-autonomous third order nonlinear differential equations are asymptotically sta... In this paper, by defining an appropriate Lyapunov functional, we obtain sufficient conditions for which all solutions of certain real non-autonomous third order nonlinear differential equations are asymptotically stable and bounded. The results obtained improve and extend some known results in the literature. 展开更多
关键词 Nonlinear Differential Equations Third Order asymptotic Stability boundedness Lyapunov Method
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DYNAMICS FOR A CHEMOTAXIS MODEL WITH GENERAL LOGISTIC DAMPING AND SIGNAL DEPENDENT MOTILITY
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作者 涂馨予 穆春来 +1 位作者 邱蜀燕 张静 《Acta Mathematica Scientia》 SCIE CSCD 2024年第3期1046-1063,共18页
In this paper,we consider the fully parabolic Chemotaxis system with the general logistic source{ut=Δ(γ(v)u)+λu-μu^(k),x∈Ω,t>0,vt=△v+wz,x∈Ω,t>0,wt=-wz,x∈Ω,t>0,zt=△z-z+u,x∈Ω,t>0 whereΩ⊂ℝn(n≥... In this paper,we consider the fully parabolic Chemotaxis system with the general logistic source{ut=Δ(γ(v)u)+λu-μu^(k),x∈Ω,t>0,vt=△v+wz,x∈Ω,t>0,wt=-wz,x∈Ω,t>0,zt=△z-z+u,x∈Ω,t>0 whereΩ⊂ℝn(n≥1)is a smooth and bounded domain,λ≥0,μ≥0,κ>1,and the motility function satisfies thatγ(v)∈C3([0,∞)),γ(v)>0,γ′(v)≤0 for all v≥0.Considering the Neumann boundary condition,we obtain the global boundedness of solutions if one of the following conditions holds:(i)λ=μ=0,1≤nλ3;(ii)λ>0,μ>0,combined withκ>1,1≤n≤3 or k>n+2/4,,n>3.Moreover,we prove that the solution (u, v, w, z) exponentially converges to the constant steady state ((λ/μ)1/k-1,∫Ωv0dx+∫Ωw0dx/|Ω|,0,(λ/μ)1/k-1). 展开更多
关键词 CHEMOTAXIS signal-dependent motility logistic source boundedness asymptotic behavior
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具有Leslie-Gower项的捕食者-食饵扩散模型的稳定性
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作者 韦创文 陈梅艳 《佛山科学技术学院学报(自然科学版)》 CAS 2024年第5期48-53,共6页
讨论具有Leslie-Gower项的捕食者-食饵弱耦合扩散系统解的一致有界性和正平衡点的稳定性。首先,应用线性化方法得出了该模型正平衡点的局部稳定性的充分条件。其次,应用Lyapunov函数方法得出了该模型正平衡点的全局渐近稳定性的充分条件。
关键词 捕食者-食饵 LESLIE-GOWER 扩散 一致有界 全局渐进稳定
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一类高阶有理差分方程的动力学定理
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作者 全卫贞 王丽 +4 位作者 周敬人 黄日娣 刘付滢 吴语桐 胡可满 《井冈山大学学报(自然科学版)》 2024年第4期7-12,共6页
根据差分方程理论,证明了高阶有理差分方程χ_(n+1)=A+Bχ_(n)/3的5个动力学定理,即唯一的正平衡解x的局部渐近稳定性、全局渐近稳定性、有界性、持续性、周期解与半循环长度等不同结论。并用计算机Matlab程序描绘此差分方程解的图像,... 根据差分方程理论,证明了高阶有理差分方程χ_(n+1)=A+Bχ_(n)/3的5个动力学定理,即唯一的正平衡解x的局部渐近稳定性、全局渐近稳定性、有界性、持续性、周期解与半循环长度等不同结论。并用计算机Matlab程序描绘此差分方程解的图像,进一步验证了这5个定理。 展开更多
关键词 差分方程 平衡解 渐近稳定性 有界性 半循环长度
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Asymptotic Stability and Boundedness for Functional Differential Equations
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作者 T.A.Burton (Department of Mathematics,Southern Illinois University,Carbondale,IL 62901-4088,U.S.A)Huang Qichang (Department of Mathematics,Northeast Normal University,Changchun 130024,China) 《Acta Mathematica Sinica,English Series》 SCIE CSCD 1997年第3期363-372,共10页
We study a system(D)x’=F(t,x_t)of functional differential equations,together with a scalar equation(S)x’=-a(t)f(x)+b(t)g(x(t-h))as well as perturbed forms.A Liapunov functional is constructed which has a derivative ... We study a system(D)x’=F(t,x_t)of functional differential equations,together with a scalar equation(S)x’=-a(t)f(x)+b(t)g(x(t-h))as well as perturbed forms.A Liapunov functional is constructed which has a derivative of a nature that has been widely discussed in the literature. On the basis of this example we prove results for(D)on asymptotic stability and equi-boundedness. 展开更多
关键词 Functional differential equations asymptotic stability boundedness Liapunov func-
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Pullback attractor of 2D non-autonomous g-Navier-Stokes equations on some bounded domains
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作者 姜金平 侯延仁 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2010年第6期697-708,共12页
The existence of the pullback attractor for the 2D non-autonomous g-Navier- Stokes equations on some bounded domains is investigated under the general assumptions of pullback asymptotic compactness. A new method to pr... The existence of the pullback attractor for the 2D non-autonomous g-Navier- Stokes equations on some bounded domains is investigated under the general assumptions of pullback asymptotic compactness. A new method to prove the existence of the pullback attractor for the 2D g-Navier-Stokes eauations is given. 展开更多
关键词 pullback attractor g-Navier-Stokes equation pullback asymptotic compactness pullback condition bounded domain
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BOUNDEDNESS,ASYMPTOTIC BEHAVIOR AND OSCILLATORY PROPERTIES FOR THE MODELS OF SINGLE-SPECIES POPULATION GROWTH WITH IMPULSIVE EFFECT
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作者 綦建刚 刘衍胜 陈绍著 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2001年第2期157-164,共8页
In this paper, we obtain the boundedness, asymptotic behavior and oscillatory properties for the single logistic models with impulse effect. Some examples are given to indicate the application of our results.
关键词 Impulse differential equations boundedness asymptotic behavior oscillatory property
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变时滞随机Lotka-Volterra生物模型的渐近性质
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作者 胡军浩 王朝航 《中南民族大学学报(自然科学版)》 CAS 北大核心 2023年第3期402-407,共6页
研究了变时滞随机Lotka-Volterra(LV)生物模型,其中变时滞函数是不可微的,放宽了现有文献变时滞是可微且导数小于1的假设.使用Itô公式和线性矩阵不等式(LMI)研究了这类生物模型全局正解的存在性和唯一性,并进一步给出了其正解渐近有界... 研究了变时滞随机Lotka-Volterra(LV)生物模型,其中变时滞函数是不可微的,放宽了现有文献变时滞是可微且导数小于1的假设.使用Itô公式和线性矩阵不等式(LMI)研究了这类生物模型全局正解的存在性和唯一性,并进一步给出了其正解渐近有界、时间均值意义下矩有界和多项式增长的充分条件.最后给出实例验证了结论的有效性. 展开更多
关键词 随机生物模型 Lotka-Volterra生物模型 不可微时滞函数 LMI不等式 渐近有界性
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具有非线性波动的运费率模型的渐近性质
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作者 连保胜 邹峰 鲁宇艺 《江苏师范大学学报(自然科学版)》 CAS 2023年第3期56-60,共5页
研究具有非线性波动的运费率模型的渐近性质.利用马尔可夫不等式,证明解的随机最终有界性.通过取适当函数,利用指数鞅不等式、Borel-Cantelli引理,得到解的轨道估计仅与模型的漂移项系数有关.最后,通过数值模拟,验证了模型的合理性.
关键词 非线性波动的运费率模型 随机最终有界性 渐近矩估计 轨道估计
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一类一阶模糊差分方程解的性态分析
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作者 欧阳苗 张千宏 陈滋利 《安徽大学学报(自然科学版)》 CAS 北大核心 2023年第3期6-15,共10页
研究一类形如x_(n+1)=Ax_(n)+Dx_(n)^(2)/Bx_(n)^(2)+Cx_(n)的具有4个模糊参数及模糊数初始条件的一阶模糊差分方程,讨论其解的性质及长时间下的发展状态.利用模糊数广义除法(g-除法),分析正解的持久性、有界性和全局渐近稳定性等性态.... 研究一类形如x_(n+1)=Ax_(n)+Dx_(n)^(2)/Bx_(n)^(2)+Cx_(n)的具有4个模糊参数及模糊数初始条件的一阶模糊差分方程,讨论其解的性质及长时间下的发展状态.利用模糊数广义除法(g-除法),分析正解的持久性、有界性和全局渐近稳定性等性态.最后通过抛物模糊数算例验证了所得结果的有效性. 展开更多
关键词 模糊差分方程 g-除法 有界性 渐近稳定
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一类具有间接信号生物趋化模型解的长时渐近行为
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作者 魏雅楠 金弘运 李静 《中央民族大学学报(自然科学版)》 2023年第4期10-18,共9页
本文利用L^(p)-L^(q)估计研究了一类具间接信号生物趋化模型■的Neumann初边值问题,得到了解的整体有界性以及长时间渐近行为。
关键词 L^(p)-L^(q)估计 整体有界性 渐近行为 间接趋化 山松甲虫模型
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