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Stability of multi-dimensional uncertain differential equation

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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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Authors and Affiliations

  1. School of Economics and Management, Tongji University, Shanghai, 200092, China

    Taoyong Su

  2. School of Statistics, Capital University of Economics and Business, Beijing, 100070, China

    Huishan Wu

  3. School of Management, Shanghai University, Shanghai, 200444, China

    Jian Zhou

Authors
  1. Taoyong Su
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  2. Huishan Wu
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  3. Jian Zhou
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Corresponding author

Correspondence to Huishan Wu.

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The authors declare that they have no competing interests.

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Communicated by V. Loia.

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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

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