STABILITY IN MEAN FOR FUZZY DIFFERENTIAL EQUATION

摘要

Fuzzy differential equation driven by Liu process is an important tool to deal with dynamic system in fuzzy environment. Stability for a fuzzy differential equation plays a key role in differential equation, which means influence of the state of a system to small changes in the initial state. In order to discuss the influence of different initial value on the solution, this paper proposes a concept of stability in mean for fuzzy differential equation driven by Liu process. Some stability theorems for fuzzy differential equation being stable in mean are given. In addition, the concept of stability in mean for fuzzy differential equation driven by Liu process is extended to the case of multi-dimensional. A sufficient condition for multi-dimensional fuzzy differential equation being stable in mean is also provided in this paper.