Exponential stability of stochastic nonlinear dynamical price system with delay

Wenli Zhu*, Xinfeng Ruan, Ye Qin, Jie Zhuang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


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 n -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.

Original languageEnglish
Article number168169
JournalMathematical Problems in Engineering
Publication statusPublished - 2013
Externally publishedYes


Dive into the research topics of 'Exponential stability of stochastic nonlinear dynamical price system with delay'. Together they form a unique fingerprint.

Cite this