Abstract
Uncertain differential equation is a type of differential equation driven by a canonical Liu process. Traditional uncertain differential equation can only deal with a continuous dynamic uncertain system. To model the sharp drifts embedded in an uncertain dynamic system, this paper proposes a type of uncertain differential equation driven by a canonical Liu process and an uncertain renewal process, which is called an uncertain differential equation with jumps. A sufficient condition for the proposed equation having a unique solution is first given, then a concept of stability for the proposed equation is provided in the sense of uncertain measure, and its sufficient condition is also derived.
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This work was supported by National Natural Science Foundation of China (Grant No. 61273044).
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Communicated by V. Loia.
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Yao, K. Uncertain differential equation with jumps. Soft Comput 19, 2063–2069 (2015). https://doi.org/10.1007/s00500-014-1392-8
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DOI: https://doi.org/10.1007/s00500-014-1392-8