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Stability of coupled impulsive Markovian jump reaction-diffusion systems on networks

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Abstract

This paper is devoted to the investigation of stability for a class of coupled impulsive Markovian jump reaction-diffusion systems on networks (CIMJRDSNs). By using graph theory, a systematic method is provided to construct global Lyapunov functions for the CIMJRDSNs. Based on Lyapunov functions and stochastic analysis method, some novel stability principles associated with the topology property of the networks are established.

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References

  1. Li M Y and Shuai Z, Global-stability problem for coupled systems of differential equations on networks, Journal of Differential Equations, 2010, 248: 248–1.

    MathSciNet  Google Scholar 

  2. Kao Y G, Wang C H, Karimi H R, et al., Global stability of coupled Markovian switching reaction-diffusion systems on networks, Nonlinear Analysis: Hybrid Systems, 2014, 13: 13–61.

    MathSciNet  MATH  Google Scholar 

  3. Kao Y G and Wang C H, Global stability analysis for stochastic coupled reaction-diffusion systems on networks, Nonlinear Analysis B: Real World Applications, 2013, 14(3): 1457–1465.

    Article  MathSciNet  MATH  Google Scholar 

  4. Cheng P and Deng F, Global exponential stability of impulsive stochastic functional differential systems, Statistics and Probability Letters, 2010, 80: 80–1854.

    Article  MathSciNet  MATH  Google Scholar 

  5. Wang C H, Kao Y G, and Yang G, Exponential stability of impulsive stochastic fuzzy reactiondiffusion Cohen-Grossberg neural networks with mixed delays, Neurocomputing, 2012, 89: 89–55.

    Article  Google Scholar 

  6. Kao Y, Wang C, and Zhang L, Delay-dependent exponential stability of impulsive Markovian jumping cohen-grossberg neural networks with reaction-diffusion and mixed delays, Neural Processing Letter, 2013, 38(3): 321–346.

    Article  Google Scholar 

  7. Zhu Q and Cao J, Stability of Markovian jump neural networks with impulse control and time varying delays, Nonlinear Analysis: Real World Applications, 2012, 13(5): 2259–2270.

    Article  MathSciNet  MATH  Google Scholar 

  8. Zhu Q and Cao J, Stability analysis of Markovian jump stochastic BAM neural networks with impulse control and mixed time delays, IEEE Transactions on Neural Networks and Learning Systems, 2012, 23(3): 467–479.

    Article  Google Scholar 

  9. Zhu Q and Cao J, Robust exponential stability of Markovian jump impulsive stochastic Cohen-Grossberg neural networks with mixed time delays, IEEE Transactions on Neural Networks and Learning Systems, 2010, 21(8): 1314–1325.

    Article  Google Scholar 

  10. Zhu Q, pth Moment exponential stability of impulsive stochastic functional differential equations with Markovian switching, Journal of Franklin Institute, 2014, 351(7): 3965–3986.

  11. Li Y and Kao Y, Stability of stochastic reaction-diffusion systems with Markovian switching and impulsive perturbations, Mathematical Problems in Engineering, 2012, DOI: 10.1155/2012/429568.

    Google Scholar 

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Authors and Affiliations

  1. School of Mathematical Sciences, Guangxi Teachers Education University, Nanning, 530001, China

    Yanbo Li

  2. Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai, 264209, China

    Yonggui Kao

Authors
  1. Yanbo Li
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  2. Yonggui Kao
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Corresponding author

Correspondence to Yonggui Kao.

Additional information

This work was supported by the National Natural Science Foundation of China under Grant Nos. 61473097, 11301090, the State Key Program of Natural Science Foundation of China under Grant No. U1533202, Shandong Independent Innovation and Achievements Transformation Fund under Grant No. 2014CGZH1101, Civil Aviation Administration of China under Grant No. MHRD20150104, and Guangxi Natural Science Foundation under Grant No. 2016JJA110005.

This paper was recommended for publication by Editor SUN Jian.

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Li, Y., Kao, Y. Stability of coupled impulsive Markovian jump reaction-diffusion systems on networks. J Syst Sci Complex 29, 1269–1280 (2016). https://doi.org/10.1007/s11424-016-4280-8

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  • DOI: https://doi.org/10.1007/s11424-016-4280-8

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