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Stochastic stability for nonlinear systems driven by Lévy noise

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Abstract

This paper is to investigate the stochastic stability for nonlinear systems with Lévy process based on Lyapunov exponents. A method of equivalent linearization is proposed to reduce and simplify the original systems. And the mean square responses are carried out to verify the effectiveness of the proposed approach. Then the Lyapunov exponents will be defined and derived to explore the stochastic stability, and two examples are presented to demonstrate the procedure of equivalent linearization and stochastic stability is considered for these two special examples. The results show that the technique of equivalent linearization can be used to study nonlinear systems excited by Lévy noise.

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Authors and Affiliations

  1. Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, 710072, China

    Yong Xu, Xi-Ying Wang, Hui-Qing Zhang & Wei Xu

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  1. Yong Xu
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  2. Xi-Ying Wang
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  3. Hui-Qing Zhang
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  4. Wei Xu
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Correspondence to Yong Xu.

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Xu, Y., Wang, XY., Zhang, HQ. et al. Stochastic stability for nonlinear systems driven by Lévy noise. Nonlinear Dyn 68, 7–15 (2012). https://doi.org/10.1007/s11071-011-0199-8

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  • DOI: https://doi.org/10.1007/s11071-011-0199-8

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