Three kinds of fixed points and stability of a class of stochastic dynamic systems
WANG Chun-sheng
LI yong-ming
Abstract：The fixed point theory has been successfully applied onto the study of zero solution stability for stochastic dynamic systems; however, the Krasnoselskii fixed point is relatively less used. In this paper, on the basis of the study for Banach and Schauder fixed point methods, we furtherly use the Krasnoselskii fixed point method to study the mean square exponential stability of zero solution in a class of stochastic dynamic systems. At the same time, we have achieved sufficient condition to make the zero solution exponential mean square of this system stable. Through the comparison of the detailed example and the conclusion in the existing articles, and comparing with Banach and Schauder fixed point methods, the Krasnoselskii fixed point is more flexible and more convenient. The conclusion in this paper has improved and extended the result of relative articles to some extent, as well as has perfected the application of fixed point methods on studying stability of zero solution in stochastic dynamical system.
Keywords：dynamical systemstabilityfixed point theoryKrasnoselskii fixed pointcompletely continuous
Publication Date：2017-01-01
Online Publishing Date：2025-08-15(First online date of this platform, not the publication date of the document)
Pages：6( 677-682 )