Nonlinear Dynamics

, Volume 70, Issue 3, pp 2107–2116 | Cite as

Globally exponential stability of stochastic neutral-type delayed neural networks with impulsive perturbations and Markovian switching

  • Yan Gao
  • Wuneng Zhou
  • Chuan Ji
  • Dongbing Tong
  • Jian’an Fang
Original Paper


The problem of globally exponential stability of stochastic neutral-type delayed neural networks with impulsive perturbations and Markovian switching is studied in this paper. By using the Lyapunov–Krasovskii method and the stochastic analysis approach, a sufficient condition to ensure globally exponential stability for the stochastic neutral-type delayed neural networks with impulsive perturbations and Markovian switching is derived. Finally, a numerical example is given to illustrate the effectiveness of the result proposed in this paper.


Neutral-type networks Impulsive perturbations Markovian switching Exponential stability Time delays 



We would like to thank the referees and the editor for their valuable comments and suggestions, which have led to a better presentation of this paper. This work is supported by the National Natural Science Foundation of China (61075060), the Innovation Program of Shanghai Municipal Education Commission (12zz064), the open project of State Key Laboratory of Industrial Control Technology, and the Fundamental Research Funds for the Central Universities.


  1. 1.
    Xu, Y., Li, B., Zhou, W., Fang, J.: Mean square function synchronization of chaotic systems with stochastic effects. Nonlinear Dynamics (2012). doi: 10.1007/s11071-011-0217-x Google Scholar
  2. 2.
    Zhao, L., Hu, J., Fang, J., Zhang, W.: Studying on the stability of fractional-order nonlinear system. Nonlinear Dynamics (2012). doi: 10.1007/s11071-012-0469-0 Google Scholar
  3. 3.
    Tang, Y., Fang, J.: Adaptive synchronization in an array of chaotic neural networks with mixed delays and jumping stochastically hybrid coupling. Commun. Nonlinear Sci. Numer. Simul. 14, 3615–3628 (2009) MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Tang, Y., Fang, J., Miao, Q.: Synchronization of stochastic delayed neural networks with Markovian switching and its application. Int. J. Neural Syst. 19, 43–56 (2009) CrossRefGoogle Scholar
  5. 5.
    Min, X., Ho, D., Cao, J.: Time-delayed feedback control of dynamical small-world networks at Hopf bifurcation. Nonlinear Dynamics 58, 319–344 (2009) MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Xu, Y., Zhou, W., Fang, J.: Topology identification of the modified complex dynamical network with non-delayed and delayed coupling. Nonlinear Dynamics 68, 195–205 (2012) MATHCrossRefGoogle Scholar
  7. 7.
    Zhou, W., Lu, H., Duan, C.: Exponential stability of hybrid stochastic neural networks with mixed time delays and nonlinearity. Neurocomputing 72, 3357–3365 (2009) CrossRefGoogle Scholar
  8. 8.
    Hassouneh, M., Abed, E.: Lyapunov and Lmi analysis and feedback control of border collision bifurcations. Nonlinear Dynamics 50, 373–386 (2007) MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Balasubramaniam, P., Nagamani, G., Rakkiyappan, R.: Passivity analysis for neural networks of neutral type with Markovian jumping parameters and time delay in the leakage term. Commun. Nonlinear Sci. Numer. Simul. 16, 4422–4437 (2011) MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    Zhang, Y., Sun, J.: Stability of impulsive neural networks with time delays. Phys. Lett. A 348, 44–50 (2005) MATHCrossRefGoogle Scholar
  11. 11.
    Xu, D., Yang, Z.: Impulsive delay differential inequality and stability of neural networks. J. Math. Anal. Appl. 305, 107–120 (2005) MathSciNetMATHCrossRefGoogle Scholar
  12. 12.
    Karthikeyan, S., Balachandran, K.: Controllability of nonlinear stochastic neutral impulsive systems. Nonlinear Anal. Hybrid Syst. 3, 266–276 (2009) MathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    Zhang, W., Tang, Y., Fang, J., Zhu, W.: Exponential cluster synchronization of impulsive delayed genetic oscillators with external disturbances. Chaos 21, 37–43 (2011) Google Scholar
  14. 14.
    Huo, H., Li, W.: Existence of positive periodic solution of a neutral impulsive delay predator-prey system. Appl. Math. Comput. 185, 499–507 (2007) MathSciNetMATHCrossRefGoogle Scholar
  15. 15.
    Park, J., Kwon, O., Lee, S.: Lmi optimization approach on stability for delayed neural networks of neutral-type. Appl. Math. Comput. 196, 236–244 (2008) MathSciNetMATHCrossRefGoogle Scholar
  16. 16.
    Park, J., Park, C., Kwon, O., Lee, S.: A new stability criterion for bidirectional associative memory neural networks of neutral-type. Appl. Math. Comput. 199, 716–722 (2008) MathSciNetMATHCrossRefGoogle Scholar
  17. 17.
    Ma, C., Wang, X.: Impulsive control and synchronization of a new unified hyperchaotic system with varying control gains and impulsive intervals. Nonlinear Dynamics (2012). doi: 10.1007/s11071-012-0476-1 Google Scholar
  18. 18.
    Tang, Y., Leung, S., Wong, W., Fang, J.: Impulsive pinning synchronization of stochastic discrete-time networks. Neurocomputing 73, 2132–2139 (2010) CrossRefGoogle Scholar
  19. 19.
    Shen, Y., Wang, J.: Robustness analysis of global exponential stability of recurrent neural networks in the presence of time delays and random disturbances. IEEE Trans. Neural Netw. Learn. Syst. 23, 87–96 (2012) CrossRefGoogle Scholar
  20. 20.
    Gu, K.: An integral inequality in the stability problem of time-delay systems. In: Proceedings of the 39th IEEE Conference on Decision and Control, vol. 3, pp. 2805–2810 (2000) Google Scholar
  21. 21.
    Berman, A., Plemmons, R.: Nonnegative Matrices in Mathematical Sciences. Academic Press, New York (1979) MATHGoogle Scholar
  22. 22.
    Bao, H., Cao, J.: Stochastic global exponential stability for neutral-type impulsive neural networks with mixed time-delays and Markovian jumping parameters. Commun. Nonlinear Sci. Numer. Simul. 16, 3786–3791 (2011) MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Yan Gao
    • 1
  • Wuneng Zhou
    • 1
  • Chuan Ji
    • 1
  • Dongbing Tong
    • 1
  • Jian’an Fang
    • 1
  1. 1.College of Information Science and TechnologyDonghua UniversityShanghaiP.R. China

Personalised recommendations