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Mathematical Problems in Engineering
Volume 2013, Article ID 168169, 9 pages
Research Article

Exponential Stability of Stochastic Nonlinear Dynamical Price System with Delay

1School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, China
2Teaching Research Training Center in Xindu District of Chengdu, Chengdu 610500, China
3Sichuan University of Science and Engineering Library, Zigong 643000, China

Received 30 January 2013; Revised 28 April 2013; Accepted 17 May 2013

Academic Editor: Wuquan Li

Copyright © 2013 Wenli Zhu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Based on Lyapunov stability theory, Itô formula, stochastic analysis, and matrix theory, we study the exponential stability of the stochastic nonlinear dynamical price system. Using Taylor's theorem, the stochastic nonlinear system with delay is reduced to an -dimensional semilinear stochastic differential equation with delay. Some sufficient conditions of exponential stability and corollaries for such price system are established by virtue of Lyapunov function. The time delay upper limit is solved by using our theoretical results when the system is exponentially stable. Our theoretical results show that if the classical price Rayleigh equation is exponentially stable, so is its perturbed system with delay provided that both the time delay and the intensity of perturbations are small enough. Two examples are presented to illustrate our results.