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New-type stability theorem for stochastic functional differential equations with application to SFDSs with distributed delays

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  • Xueyan Zhao
  • Feiqi Deng

Abstract

In this paper, a new-type stability theorem for stochastic functional differential equations (SFDEs) is established, which is not a direct copy of the basic stability theorem for deterministic functional differential equations (DFDEs). By the new-type stability theorem, one can use the most simple Lyapunov functions and employ the equations repeatedly to deal with the delayed terms encountered conveniently and to carry out stability criteria for the equations. Based on the theorem, a practical stability theorem in accordance with the Lyapunov function method is also established, and then the asymptotic stability of SFDEs with distributed delays in the diffusive terms is investigated and a stability criterion for SFDSs is obtained, which is described by algebraic matrix equations. Finally, an example is given to illustrate the effectiveness of our method and results.

Suggested Citation

  • Xueyan Zhao & Feiqi Deng, 2014. "New-type stability theorem for stochastic functional differential equations with application to SFDSs with distributed delays," International Journal of Systems Science, Taylor & Francis Journals, vol. 45(5), pages 1156-1169, May.
    • Handle: RePEc:taf:tsysxx:v:45:y:2014:i:5:p:1156-1169
    DOI: 10.1080/00207721.2012.745028
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    References listed on IDEAS

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    1. Lei Liu & Yi Shen & Feng Jiang, 2012. "Delay-dependent exponential stability of stochastic delay differential system whose coefficients obey the polynomial growth condition," International Journal of Systems Science, Taylor & Francis Journals, vol. 43(9), pages 1664-1672.
    2. Wang, Kai & Teng, Zhidong & Jiang, Haijun, 2008. "Adaptive synchronization of neural networks with time-varying delay and distributed delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(2), pages 631-642.
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