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首页> 外文期刊>Journal of Computational and Applied Mathematics >Stability of equilibrium states for a stochastically perturbed exponential type system of difference equations
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Stability of equilibrium states for a stochastically perturbed exponential type system of difference equations

机译：差分方程的随机摄动指数型系统平衡态的稳定性

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摘要

In the paper it is shown how the known results of stability theory can be simply applied to stability investigation of equilibrium points of some systems of nonlinear difference equations with stochastic perturbations. A system of two difference equations with exponential nonlinearity is considered and it is shown that instead of the zero equilibrium this system can have also a positive equilibrium. Sufficient conditions for stability in probability of the both equilibriums of the initial nonlinear system with stochastic perturbations are obtained. Numerical simulations and figures illustrate a convergence of the positive solutions of the considered system to one of two (zero or positive) equilibriums in deterministic and stochastic cases. The proposed investigation procedure can be applied for arbitrary nonlinear equations with an order of nonlinearity higher than one. (C) 2015 Elsevier B.V. All rights reserved.
机译：本文显示了如何将已知的稳定性理论的结果简单地应用于一些具有随机扰动的非线性差分方程系统的平衡点的稳定性研究。考虑了一个具有指数非线性的两个差分方程组，结果表明，代替零平衡，该系统也可以具有一个正平衡。获得了具有随机扰动的初始非线性系统的两个平衡的概率稳定性的充分条件。数值模拟和数字说明了在确定性和随机情况下，所考虑系统的正解收敛于两个（零或正）平衡之一。所提出的研究程序可以应用于非线性阶数大于1的任意非线性方程组。 （C）2015 Elsevier B.V.保留所有权利。

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