Affiliations: [a] College of Information Science and Engineering, Xinjiang University, Urumqi, China
| [b] School of Management and Engineering, Capital University of Economics and Business, Beijing, China
Correspondence:
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Corresponding authors: Gang Shi, College of Information Science and Engineering, Xinjiang University, Urumqi 830046, China. E-mail: [email protected] and Lifen Jia, School of Management and Engineering, Capital University of Economics and Business, Beijing 100084, China. E-mail: [email protected].
Abstract: Uncertain differential equation plays an important role in dealing with dynamical systems with uncertainty. Multi-dimensional uncertain differential equation is a type of differential equation driven by multi-dimensional Liu processes. Stability analysis of a multi-dimensional means insensitivity of the state of a system to small changes in the initial state. This paper focuses on the stability in p-th moment for multi-dimensional uncertain differential equation. The concept of stability in p-th moment for multi-dimensional uncertain differential equation is presented. Some stability theorems for the solution of multi-dimensional uncertain differential equation are given, in which some sufficient conditions for a multi-dimensional uncertain differential equation being stable in p-th moment and a sufficient and necessary condition for a linear multi-dimensional uncertain differential equation being stable in p-th moment are provided. In addition, this paper discusses the relationships among stability in p-th moment, stability in measure and stability in mean.
Keywords: Uncertainty theory, multi-dimensional uncertain differential equation, moment stability
