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11MroductlonThe purpose ofthls paper Is to Investigate eWone尬lal stability of*theity mild solutions forcenain Hilbert space-Mued stochastlc evoMlon eqll砒ions,Roughy spe出0ng;we cons讪r山efollowing equation:I 伏I=*x,+风Il加L十从L,剧dWn,c〔瓜+咖。(””””“”(11)D 人n 二x.Where A Is the Infinlteslmalgener砒or ofa certain几semigroup S(t),t>0;on H and F(t;、)and B(t;·)are In general nonlinear mappings from H to H and H to L(x,H),the family ofall bounded linear operators from … 相似文献
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针对一类变延迟微分方程,应用全隐式方法一平衡方法,研究了其收敛性和稳定性.结果表明平衡方法以1/2 γ,γ∈(0,1]阶收敛到精确解;并且强平衡方法和弱平衡方法都能保持解析解的均方稳定性;进一步数值实验验证了算法理论分析的正确性,并且表明全隐式的平衡方法比显式方法—Euler方法具有更好的稳定性. 相似文献
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Jili Wang Linshan Wang 《Annals of Differential Equations》2014,(2):184-190
In this paper, the stability in Lagrange sense of a class of stochastic static neural networks with mixed time delays is studied. Based on the Lyapunov stability theory and with the help of stochastic analysis technique, the criteria for the stability in Lagrange sense of stochastic static neural networks with mixed time delays is obtained. One example is given to verify the advantage and applicability of the proposed results. 相似文献
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In this paper,we obtain suffcient conditions for the stability in p-th moment of the analytical solutions and the mean square stability of a stochastic differential equation with unbounded delay proposed in [6,10] using the explicit Euler method. 相似文献
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Lu Xiaomei Chen Wuhua Wang Lili 《Annals of Differential Equations》2005,21(3):366-369
In this paper, the stability properties for a class of switched stochastic systems with commutative componentwise subsystem matrices are studied. Under some switching law, the trivial solutions of the above systems are proved to be exponentially stable in mean square and almost sure exponentially stable if the random perturbations are sufficiently "small". 相似文献
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给出了一类中立型随机泛函方程的随机一致稳定性的充分条件,利用了新的分析技巧处理中立型时滞项,得到了中立型随机时滞泛函微分方程渐近稳定性的充分判据.在处理各种渐近估计是有效的. 相似文献
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本文讨论一般非线性随机延迟微分方程Heun方法的数值稳定性,证明了如果问题本身满足零解是均方指数稳定和均方渐近稳定的充分条件,则当方程的漂移项进一步满足一定的条件时,Heun方法是Ms.稳定的,带线性插值的Heun方法是均方指数稳定的和GMS-稳定的理论结果.文末的数值试验进一步验证了所得的相关结论. 相似文献
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In this paper, the problem of partial equiasymptotic stability for nonlinear time-varying differential equations are analyzed. A sufficient condition of partial stability and a set of sufficient conditions of partial equiasymptotic stability are given. Some of these conditions allow the derivative of Lyapunov function to be positive. Finally, several numerical examples are also given to illustrate the main results. 相似文献
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In this paper,by constructing proper Lyapunov functions,exponential stability criteria for stochastic delay partial differential equations are obtained. An example is shown to illustrate the results. 相似文献
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EVANS FUNCTIONS AND INSTABILITY OF A STANDING PULSE SOLUTION OF A NONLINEAR SYSTEM OF REACTION DIFFUSION EQUATIONS
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Linghai Zhang 《应用数学年刊》2016,32(1):79-101
In this paper, we consider a nonlinear system of reaction diffusion equations arising from mathematical neuroscience and two nonlinear scalar reaction diffusion equations under some assumptions on their coefficients. The main purpose is to couple together linearized stability criterion (the equivalence of the nonlinear stability, the linear stability and the spectral stability of the standing pulse solutions) and Evans functions to accomplish the existence and instability of standing pulse solutions
of the nonlinear system of reaction diffusion equations and the nonlinear scalar reaction diffusion equations. The Evans functions for the standing pulse solutions are constructed explicitly. 相似文献
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GENERALIZED SOLUTION OF SINGULARLY PERTURBED PROBLEMS FOR REACTION DIFFUSION EQUATIONS 总被引:2,自引:0,他引:2
Yao Jingsun Mo Jiaqi 《Annals of Differential Equations》2006,22(1):81-86
The singularly perturbed initial boundary value problem for reaction diffusion equation is considered. Under suitable conditions the existence, uniqueness and asymptotic behavior of the generalized solution for the problems are studied. 相似文献
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本文研究一类线性随机延迟积分微分方程Euler-Maruyama方法的MS-稳定性.首先,我们讨论方程真解的均方指数稳定性条件.然后,在此假设条件下,证明了带有复合梯形公式的Euler-Maruyama方法是MS-稳定的.最后,数值试验验证了本文的结论. 相似文献
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莫嘉琪 《数学物理学报(B辑英文版)》2003,23(3)
A class of nonlinear singularly perturbed problems for reaction diffusion equa-tions are considered. Under suitable conditions, by using the theory of differential inequal-ities, the asymptotic behavior of solutions for the initial boundary value problems arestudied, reduced problems of which possess two intersecting solutions. 相似文献
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一类微分-差分反应扩散方程的渐近解 总被引:1,自引:0,他引:1
本文研究了一类带有小延迟的微分-差分反应扩散方程初值问题.利用奇摄动伸长变量法以及微分不等式理论,构造了问题的形式渐近解,并证明了解的一致有效性. 相似文献
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本文讨论Euler方法用于求解线性中立型随机延迟微分方程初值问题时数值解的稳定性,利用了一种不同于以往文献中的证明技巧,给出了Euler方法均方稳定的一个充分条件.文末的数值试验证实了本文所获理论结果的正确性. 相似文献
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一类脉冲微分方程零解的稳定性 总被引:2,自引:0,他引:2
本文研究了一类在非固定时刻的脉冲微分方程。利用Lyapunov第二方法,建立了零解为稳定,渐近稳定及不稳定的判别准则。结果表明脉冲可能影响甚至改变相应的无脉冲时的微分方程的稳定性。文中还给出一例说明所得主要结果的应用。 相似文献