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Stochastic Hybrid System with Polynomial Growth Coefficients

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Abstract

The environmental and telegraph noise may be beneficial in the cognitive systems. In this paper, we will study a class of nonlinear system with Markovian switching, whose coefficients satisfy the one-sided polynomial growth condition and the local Lipschitz condition. This paper shows that the Brownian motion may suppress the potential explosion of the solution of the deterministic nonlinear system under some conditions. Moreover, another Brownian motion may exponentially stabilize the system. Finally, an example is given to illustrate our results.

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Acknowledgments

The work is supported by the Fundamental Research Funds for the Central Universities under Grant 2012089, Zhongnan University of Economics and Law and China Postdoctoral Science Foundation funded project under Grant 2012M511615.

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Authors and Affiliations

  1. Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan, 430074, China

    Lizhu Feng

  2. School of Mathematics and Computer Science, Jianghan University, Wuhan, 430056, China

    Lizhu Feng

  3. School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan, 430073, China

    Feng Jiang

  4. School of Measuring and Optoelectronic Engineering, Nanchang Hangkong University, Nanchang, Jiangxi, 330063, China

    Feng Li

Authors
  1. Lizhu Feng
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  2. Feng Jiang
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Correspondence to Lizhu Feng.

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Feng, L., Jiang, F. & Li, F. Stochastic Hybrid System with Polynomial Growth Coefficients. Cogn Comput 5, 32–39 (2013). https://doi.org/10.1007/s12559-012-9149-0

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  • DOI: https://doi.org/10.1007/s12559-012-9149-0

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