共查询到20条相似文献,搜索用时 429 毫秒
1.
Yonghui Xi Huicheng Wang Kit Ian Kou Zhaoping Hu 《Journal of Applied Analysis & Computation》2016,6(3):893-906
The main purpose of this article is to study the periodicity of a Lotka-Volterra''s competition system with feedback controls. Some new and interesting sufficient conditions are obtained for the global existence of positive periodic solutions. Our method is base on combining matrix''s spectral theory and inequality $|x(t)|\leq x(t_{0})+\int_{0}^{\omega }|\dot{x}(t)|{\rm d}t$. Some examples and their simulations show the feasibility of our main result. 相似文献
2.
一类三阶非线性系统的全局渐近稳定性 总被引:8,自引:0,他引:8
对一类三阶非线性系统构造出了较好的Lyapunov函数,得到其零解全局渐近稳定的充分性准则,而且去掉了一般要求Lyapunov函数具有无穷大这个较强的条件,只要求系统正半轨线有界,所得结果包含并改进了旧有的结果. 相似文献
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在运用Lyapunov函数第二方法研究非线性系统稳定性的时候,能否做出合适的Lya- punov函数是问题的关键,本文对三阶非线性系统x g(x)x f(x,x) h(x)=0构造出了较好的Lyapunov函数,得到其零解全局渐近稳定的充分性准则,它包含并改进了这一形式非线性系统的大部分结果. 相似文献
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G. Leitmann 《Journal of Optimization Theory and Applications》1979,27(1):99-106
We consider a class of linear dynamical systems with bounded, Lebesgue-measurable uncertainties in the system and input matrices as well as in the input itself. A state feedback control is derived, which guarantees global, uniform asymptotic stability of the zero state; this control is continuous, except at the zero state.This paper is based in part on research supported by the National Science Foundation. 相似文献
6.
Wu Yaping 《偏微分方程(英文版)》1990,3(4)
ln this paper, the order of magnitude and structure of nonnegative solutions for a class of R-D systems with 3 components is obtained. Especially for the case α_2 =α_3 a complete analysis is given. By using different method from [1], a simpler and more concrete sufficient condition for uniqueness and globally asymptotic stability of nonnegative solution is also obtained. 相似文献
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关于滞后型泛函微分方程的稳定性,本文给出了更一般的判别准则,推广了Paзyмихин的结果。并将所得结论用于考察具有缓变系数的线性时滞系统的稳定性,放宽了通常的对系统系数矩阵特征值的限制,给出了直接由系统右端系数计算的简明的稳定性判据。 相似文献
9.
Tingxiu Wang 《Journal of Mathematical Analysis and Applications》2006,324(2):982-991
With the Lyapunov second method, we study the abstract functional differential equation, . We obtain inequalities of solutions and exponential stability with conditions like:
- (i)
- ,
- (ii)
- .
10.
This paper is concerned with a equation, which is a model of filtration in partially saturated porous media, with mixed boundary condition of Dirichlet-Neumann type {∂_tb(u) - ∇ • a [∇u + k(b(u))] = f \qquad in \quad (0, ∞) × Ω u = h(t, x) \qquad on \quad (0, ∞) × Γ_0 v • a [∇u + k(b(u))] = g(t, x) \qquad on \quad (0, ∞) × Γ_1 We have proved that there exists one and only one periodic solution of the problem under the data f, g and h with same period. Moreover, we have proved that the unique periodic solution ω is asymptotically statble in the sense that for any solution u of the problem b(u(t)) - b(ω(t)) → 0\qquad in L²(Ω) as t → ∞. 相似文献
11.
A. Yu. Aleksandrov 《Mathematical Notes》1998,63(1):3-8
We study systems of differential equations with perturbations that are unbounded functions of time. We suggest a method for
constructing Lyapunov functions to determine conditions under which the perturbations do not affect the asymptotic stability
of the solutions.
Translated fromMatematicheskie Zametki, Vol. 63, No. 1, pp. 3–8, January, 1998. 相似文献
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Masakazu Onitsuka 《Applied mathematics and computation》2011,218(4):1436-1442
In this paper, sufficient conditions for uniform asymptotic stability of the damped linear oscillators with variable coefficients are presented. The result of the present study can be applied to even the case of negative damping. The conditions presented herein are shown to be essential for uniform asymptotic stability. 相似文献
14.
Josef Kalas 《Mathematische Nachrichten》2010,283(6):879-890
The asymptotic behaviour and stability properties are studied for a real two‐dimensional system x′(t) = A(t)x (t) + B(t)x (θ (t)) + h (t, x (t), x (θ (t))), with a nonconstant delay t ‐ θ (t) ≥ 0. It is supposed that A,B and h are matrix functions and a vector function, respectively. The method of investigation is based on the transformation of the considered real system to one equation with complex‐valued coefficients. Stability and asymptotic properties of this equation are studied by means of a suitable Lyapunov‐Krasovskii functional. The results generalize the great part of the results of J. Kalas and L. Baráková [J. Math. Anal. Appl. 269 , No. 1, 278–300 (2002)] for two‐dimensional systems with a constant delay (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
15.
We consider the quasilinear systems of difference equations with periodic coefficients in linear terms. We obtain estimates for the attraction domain of the zero solution and establish inequalities for the norms of solutions. The results are stated in terms of Lyapunov-type matrix series. 相似文献
16.
We consider a quasilinear system of differential equations with periodic coefficients in the linear terms. We obtain estimates for the attraction domain of the zero solution and establish estimates for the decay rate of solutions at infinity. The results are stated in terms of the integrals of the norm of a periodic solution to the Lyapunov differential equation. 相似文献
17.
A. O. Ignatyev 《Proceedings of the American Mathematical Society》1999,127(6):1753-1760
Consider a system of functional differential equations where is the vector-valued functional. The classical asymptotic stability result for such a system calls for a positive definite functional and negative definite functional . In applications one can construct a positive definite functional , whose derivative is not negative definite but is less than or equal to zero. Exactly for such cases J. Hale created the effective asymptotic stability criterion if the functional in functional differential equations is autonomous ( does not depend on ), and N. N. Krasovskii created such criterion for the case where the functional is periodic in . For the general case of the non-autonomous functional V. M. Matrosov proved that this criterion is not right even for ordinary differential equations. The goal of this paper is to prove this criterion for the case when is almost periodic in . This case is a particular case of the class of non-autonomous functionals.
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借助Lyapunov函数方法 ,讨论了一类分离变量系统的全局稳定性和全局指数稳定性 ,得到了由系统自身特点所给出的几个显示代数判据 ,这些充分性结论为实际应用提供方便 ,推广了有关文献中的一些结果 . 相似文献
20.
MengFAN KeWANG PatriciaJ.Y.WONG RaviP.AGARWAL 《数学学报(英文版)》2003,19(4):801-822
By using the method of coincidence degree and Lyapunov functional, a set of easily applicable criteria are established for the global existence and global asymptotic stability of strictly positive(componentwise)periodic solution of a periodic n-species Lotka-Volterra competition system with feedback controls and several deviating arguments.The problem considered in this paper is in many aspects more general and incorporate as special cases various problems which have been studied extensively in the literature.Moreover,our new criteria,which improve and generalize some well known results, can be easily checked. 相似文献