共查询到20条相似文献,搜索用时 109 毫秒
1.
微分方程的指数稳定性 总被引:1,自引:0,他引:1
比较系统地研究了It方程解的指数稳定性.给出了随机指数稳定性、指数P-稳定性、几乎必然指数稳定性的比较准则,这些比较准则推广了Nevel’son和Has’minskiǐ的相应结果. 相似文献
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《数学的实践与认识》2017,(16)
研究了具有时间滞后切换不确定细胞神经网络(UCNNs)系统的指数稳定性.利用同胚映射和M矩阵理论,得到UCNNs系统平衡点存在性,唯一性和指数稳定性的充分条件;利用平均驻留时间方法,研究了时滞切换UCNNs系统限制切换下的鲁棒指数稳定性,并得到确保系统全局指数稳定的充分条件. 相似文献
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泛函微分方程的Lipschitz指数稳定性 总被引:4,自引:0,他引:4
提出泛函微分方程的Lipschitz指数稳定性概念,给出了利用Liapunov泛函数研究Lipschitz指数稳定性的条件。 相似文献
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利用退化半群的方法讨论了Hilbert空间中一阶广义分布参数系统的指数稳定性,并给出了判断指数稳定性的充要条件. 相似文献
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本文采用Lyapunov-Krasovskii泛函方法对一类变时滞细胞神经网络的全局指数稳定性进行了研究,得出了一些关于DCNN全局指数稳定性的充分条件。 相似文献
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收稿研究了一类带多个小滞量的非线性延迟微分方程的指数稳定性,证明了在适当条件下,上述延迟微分方程可保留相应常微分方程的指数稳定性.所获稳定性判据修正和扩展了已有延迟微分方程的相关结果.在文末,数值例子进一步阐明了其稳定性理论. 相似文献
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Ravi P. Agarwal Alexander Domoshnitsky Abraham Maghakyan 《Czechoslovak Mathematical Journal》2015,65(4):1047-1068
We propose a new method for studying stability of second order delay differential equations. Results we obtained are of the form: the exponential stability of ordinary differential equation implies the exponential stability of the corresponding delay differential equation if the delays are small enough. We estimate this smallness through the coefficients of this delay equation. Examples demonstrate that our tests of the exponential stability are essentially better than the known ones. This method works not only for autonomous equations but also for equations with variable coefficients and delays. 相似文献
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Pham Huu Anh Ngoc 《Mathematische Nachrichten》2014,287(7):803-824
General linear functional differential equations with infinite delay are considered. We first give an explicit criterion for positivity of the solution semigroup of linear functional differential equations with infinite delay and then a Perron‐Frobenius type theorem for positive equations. Next, a novel criterion for the exponential asymptotic stability of positive equations is presented. Furthermore, two sufficient conditions for the exponential asymptotic stability of positive equations subjected to structured perturbations and affine perturbations are provided. Finally, we applied the obtained results to problems of the exponential asymptotic stability of Volterra integrodifferential equations. To the best of our knowledge, most of the results of this paper are new. 相似文献
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Haiyan Yuan 《计算数学(英文版)》2022,40(2):177-204
In this paper, the numerical methods for semi-linear stochastic delay integro-differential equations are studied. The uniqueness, existence and stability of analytic solutions of semi-linear stochastic delay integro-differential equations are studied and some suitable conditions for the mean-square stability of the analytic solutions are also obtained. Then the numerical approximation of exponential Euler method for semi-linear stochastic delay integro-differential equations is constructed and the convergence and the stability of the numerical method are studied. It is proved that the exponential Euler method is convergent with strong order $\frac{1}{2}$ and can keep the mean-square exponential stability of the analytical solutions under some restrictions on the step size. In addition, numerical experiments are presented to confirm the theoretical results. 相似文献
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《Applied Mathematics Letters》2007,20(8):839-845
This work studies global exponential stability of impulsive delay differential systems. By employing the Razumikhin technique and Lyapunov functions, several global exponential stability criteria are established for general impulsive delay differential equations. Our results show that delay differential equations may be exponentially stabilized by impulses. An example and its simulation are also given to illustrate our results. 相似文献
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Lijun Pan 《Journal of Mathematical Analysis and Applications》2011,382(2):672-685
In this paper, we investigate the pth moment and almost sure exponential stability of impulsive stochastic functional differential equations with finite delay by using Lyapunov method. Several stability theorems of impulsive stochastic functional differential equations with finite delay are derived. These new results are employed to impulsive stochastic equations with bounded time-varying delays and stochastically perturbed equations. Meanwhile, an example and simulations are given to show that impulses play an important role in pth moment and almost sure exponential stability of stochastic functional differential equations with finite delay. 相似文献
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研究了一类G-Brown运动驱动的中立型随机时滞微分方程的指数稳定性.在G-框架意义下,运用合适的Lyapunov-Krasovskii泛函,中立型时滞微分方程理论以及随机分析技巧,证明了所研究方程平凡解的p-阶矩指数稳定性,得到了所研究方程平凡解是p-阶矩指数稳定的充分条件.最后通过例子说明所得的结果. 相似文献
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The exponential asymptotic stability of singularly perturbed delay differential equations with a bounded lag 总被引:1,自引:0,他引:1
Hongjiong Tian 《Journal of Mathematical Analysis and Applications》2002,270(1):143-149
This paper is concerned with the exponential stability of singularly perturbed delay differential equations with a bounded (state-independent) lag. A generalized Halanay inequality is derived in Section 2, and in Section 3 a sufficient condition will be provided to ensure that any solution of the singularly perturbed delay differential equations (DDEs) with a bounded lag is exponentially stable uniformly for sufficiently small ε>0. This type of exponential asymptotic stability can obviously be applied to general delay differential equations with a bounded lag. 相似文献
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《Nonlinear Analysis: Real World Applications》2007,8(1):375-398
A mathematical model of a single isolated artificial neuron with hysterisis is formulated by means of a neutral delay differential equation. The asymptotic and exponential stability of such a model are investigated. Sufficient conditions for the exponential stability of a linear integral difference inequality are obtained. In the absence of hysterisis effect, our model reduces to a known model of a single neuron. Usually asymptotic stability of neutral delay differential equations is studied by means of degenerate Lyapunov–Kravsovskii functionals. In this article, perhaps for the first time exponential stability of a class of neutral differential equations are studied by means of the exponential stability of an affiliated difference inequality. While generalization to Hopfield type hysteretic neural networks is possible, such a generalization is not considered in this article. 相似文献
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Exponential stability of nonlinear differential equations in the presence of perturbations or delays
《Communications in Nonlinear Science & Numerical Simulation》2007,12(6):869-875
The exponential stability of nonlinear nonautonomous nonsmooth differential equations in finite dimensional linear spaces is investigated. It turns out that exponential stability is preserved under sufficiently small perturbations or delays. Explicit estimates for the relation between the exponential decay rates and the size of the perturbation or delay are presented. The results are valid for differential equations given by Lipschitz continuous vector fields. 相似文献
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Svetlana Jankovi? 《Journal of Mathematical Analysis and Applications》2009,355(2):811-6134
The paper discusses both pth moment and almost sure exponential stability of solutions to neutral stochastic functional differential equations and neutral stochastic differential delay equations, by using the Razumikhin-type technique. The main goal is to find sufficient stability conditions that could be verified more easily then by using the usual method with Lyapunov functionals. The analysis is based on paper [X. Mao, Razumikhin-type theorems on exponential stability of neutral stochastic functional differential equations, SIAM J. Math. Anal. 28 (2) (1997) 389-401], referring to mean square and almost sure exponential stability. 相似文献