Abstract
Multi-dimensional uncertain differential equation is used to model a multi-dimensional dynamic uncertain system. In order to describe the influence of the initial value on the solution, this paper proposes a concept of stability for multi-dimensional uncertain differential equation. A sufficient condition is derived for a multi-dimensional uncertain differential equation being stable, and its effectiveness is illustrated by some examples. In addition, this paper shows that the given condition is not necessary for a multi-dimensional uncertain differential equation being stable via a counterexample. The results presented in this paper could be used to study the stability of multi-factor uncertain differential equations and high-order uncertain differential equations.
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Acknowledgments
This work was supported by the Humanities and Social Science Foundation of the Ministry of Education of China (10YJC63021), National Natural Science Foundation of China (No. 71402121).
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Su, T., Wu, H. & Zhou, J. Stability of multi-dimensional uncertain differential equation. Soft Comput 20, 4991–4998 (2016). https://doi.org/10.1007/s00500-015-1788-0
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DOI: https://doi.org/10.1007/s00500-015-1788-0