JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2016, Vol. 51 ›› Issue (2): 29-36.doi: 10.6040/j.issn.1671-9352.0.2015.271

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Stochastic suppression on explosive solutions of a class of nonlinear impulsive differential systems by noise

ZHANG Chun-yan1, HAO Sheng-nan1*, FENG Li-chao2   

  1. 1. College of Information Engineering, North China University of Science and Technology, Tangshan 063009, Hebei, China;
    2. College of Science, North China University of Science and Technology, Tangshan 063009, Hebei, China
  • Received:2015-06-08 Online:2016-02-16 Published:2016-03-11

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Abstract: We investigate the problem of stochastic suppression on explosive solutions of nonlinear impulsive differential systems by noise. For a given nonlinear impulsive differential system satisfying one-sided polynomial growth condition which may explode at a finite time, we introduce a polynomial stochastic noise σ|x(t)|βx(t)dB(t)(B(t)is a Brownian motion)such that there exists a unique global solution for the corresponding stochastically perturbed impulsive differential system. The global solution is bounded in the sense of the moment and the trajectory with large probability and the global solution grow at most polynomial.

Key words: one-sided polynomial growth condition, impulsive differential systems, Itó formula, stochastic noise, explosive solutions

CLC Number: 

  • O231.3
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