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Synchronization of Reaction–Diffusion Stochastic Complex Networks

  • Chaolong Zhang
  • Feiqi DengEmail author
  • Xisheng Dai
  • Shixian Luo
Original Paper
  • 17 Downloads

Abstract

Based on the LaSalle invariant principle of stochastic differential delay equations and Wirtinger’s inequality as well as periodically intermittent control and impulsive control schemes, several sufficient conditions ensuring the synchronization of stochastic complex networks with reaction–diffusion and varying delays are obtained. The Wirtinger inequality overcomes the conservatism introduced by the integral inequality used in the previous results. The proposed criterion for synchronization generalizes and improves those reported recently in the literature. Finally, an illustrative example is given to show effectiveness of results.

Keywords

Stochastic Synchronization Reaction–diffusion Periodically intermittent Impulsive 

Notes

Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grants 61573156, 61273126, 61503142, and Natural Science Foundation of Guangdong Province under Grant 2015A030310065 ,and Science and Technology Plan Foundation of Guangzhou under Grant 201704030131.

References

  1. 1.
    Carroll, T.L., Pecora, L.M.: Synchronization chaotic circuits. IEEE Trans. Circ. Syst. 38, 453–6 (1991)CrossRefGoogle Scholar
  2. 2.
    Pecora, L.M., Carroll, T.L.: Synchronization in chaotic systems. Phys. Rev. Lett. 64, 821–4 (1990)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Yang, T., Chua, L.O.: Impulsive stabilization for control and synchronization of chaotic system: theory and application to secure communication. IEEE Trans. Circuits Syst. I(44), 976–988 (1997)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Cao, J., Wang, Z., Sun, Y.: Synchronization in an array of linearly stochastically coupled networks with time delays. Physica A 385, 718–728 (2008)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Hu, C., Jiang, H., Teng, Z.: Impulsive control and synchronization for delayed neural networks with reaction–diffusion terms. IEEE Trans. Neural Netw. 21, 67–81 (2010)CrossRefGoogle Scholar
  6. 6.
    Wang, K., Teng, Z., Jiang, H.: Global exponential synchronization in delayed reaction–diffusion cellular neural networks with the Dirichlet boundary conditions. Math. Comput. Model. 52, 12–24 (2010)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Yu, F., Jiang, H.: Global exponential synchronization of fuzzy cellular neural networks with delays and reaction–diffusion terms. Neurocomputing 74, 509–515 (2011)CrossRefGoogle Scholar
  8. 8.
    Yu, W., Cao, J., Lu, W.: Synchronization control of switched linearly coupled neural networks with delay. Neurocomputing 73, 858–866 (2010)CrossRefGoogle Scholar
  9. 9.
    Li, Z., Jiao, L., Lee, J.: Robust adaptive global synchronization of complex dynamical networks by adjusting time-varying coupling strength. Physica A 387, 1369–1380 (2008)CrossRefGoogle Scholar
  10. 10.
    Huang, L., Wang, Z., Wang, Y., Zuo, Y.: Synchronization analysis of delayed complex networks via adaptive time-varying coupling strengths. Phys. Lett. A 373, 3952–3958 (2009)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Xu, J., Tan, Y.: A composite energy function based learning control approach for nonlinear systems with time-varying parametric uncertainties. IEEE Trans. Automat. Control 47, 1940–1945 (2002)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Wang, T., Li, J., Tang, S.: Adaptive synchronization of nonlinearly parameterized complex dynamical networks with unknown time-varying parameters. Math. Probl. Eng. 2012, 16 (2012).  https://doi.org/10.1155/2012/592539 MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Guo, X., Li, J.: A new synchronization algorithm for delayed complex dynamical networks via adaptive control approach. Commun. Nonlinear Sci. Numer. Simul. 17, 4395–4403 (2012)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Song, Q., Cao, J.: On pinning synchronization of directed and undirected complex dynamical networks. IEEE Trans. Circuits Syst. I Regul. Pap. 57(3), 672–680 (2010)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Lu, J., Cao, J., Ho, D.: Adaptive stabilization and synchronization for chaotic Lure systems with time-varying delay. IEEE Trans. Circuits Syst. I Regul. Pap. 55(5), 1347–1356 (2008)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Yang, X., Cao, J., Lu, J.: Synchronization of coupled neural networks with random coupling strengths and mixed probabilistic time-varying delays. Int. J. Robust Nonlinear Control 23(18), 2060–2081 (2013)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Yang, X., Cao, J., Lu, J.: Synchronization of randomly coupled neural networks with Markovian jumping and time-delay. IEEE Trans. Circuits Syst. I Regul. Pap. 60(2), 363–376 (2013)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Serrano-Gotarredona, T., Linares-Barrnco, B.: Log-domain implementation of complex dynamics reaction–diffusion neural network. IEEE Trans. Neural Netw. 14(5), 1337–1355 (2003)CrossRefGoogle Scholar
  19. 19.
    Akca, H., Covachev, V.: Spatial discretization of an impulsive Cohen–Grossberg neural network with time-varying and distributed delays and rection–diffusion terms. Ann. St. Univ. Ovidius Constanta 17(3), 15–26 (2009)zbMATHGoogle Scholar
  20. 20.
    Liu, X.: Synchronization of linearly coupled neural networks with reaction–diffusion terms and unbounded time delays. Neurocomputing 73, 2681–2688 (2010)CrossRefGoogle Scholar
  21. 21.
    Blythe, S., Mao, X., Liao, X.: Stability of stochastic delay neural networks. J. Frankl. Inst. 338, 481–495 (2001)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Kwon, O.M., Lee, S.M., Park, J.H.: Improved delay-dependent exponential stability for uncertain stochastic neural networks with time-varying delays. Phys. Lett. A 374, 1232–1241 (2010)CrossRefGoogle Scholar
  23. 23.
    Yang, X., Cao, J., Xu, C., Feng, J.: Finite-time stabilization of switched dynamical networks with quantized couplings via quantized controller. Sci. China Technol. Sci. 61(2), 299–308 (2018)CrossRefGoogle Scholar
  24. 24.
    Chen, W., Yang, W., Zheng, W.: Adaptive impulsive observers for nonlinear systems: revisited. Automatica 61, 232–240 (2015)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Chen, W., Wei, D., Lu, X.: Global exponential synchronization of nonlinear time-delay Lure systems via delayed impulsive control. Commun. Nonlinear Sci. Numer. Simulat. 19, 3298–3312 (2014)CrossRefGoogle Scholar
  26. 26.
    Chen, W., Lu, X., Zheng, W.: Impulsive stabilization and impulsive synchronization of discrete-time delayed neural networks. IEEE Trans. Neural Netw. Learn. Syst. 26(4), 734–748 (2015)MathSciNetCrossRefGoogle Scholar
  27. 27.
    Fu, X., Li, X.: LMI conditions for stability of impulsive stochastic Cohen–Grossberg neural networks with mixed delays. Commun. Nonlinear Sci. Numer. Simulat. 16, 435–454 (2011)MathSciNetCrossRefGoogle Scholar
  28. 28.
    Ma, T., Fu, J.: On the exponential synchronization of stochastic impulsive chaotic delayed neural networks. Neurocomputing 74, 857–862 (2011)CrossRefGoogle Scholar
  29. 29.
    Yang, X., Cao, J., Lu, J.: Synchronization of delayed complex dynamical networks with impulsive and stochastic effects. Nonlinear Anal. Real World Appl. 12(4), 2252–2266 (2011)MathSciNetCrossRefGoogle Scholar
  30. 30.
    Yang, X., Lu, J., Ho, D., Song, Q.: Synchronization of uncertain hybrid switching and impulsive complex networks. Appl. Math. Model. 59, 379–392 (2018)MathSciNetCrossRefGoogle Scholar
  31. 31.
    Yang, X., Xu, C., Feng, J., Lu, J.: General synchronization criteria for nonlinear Markovian systems with random delays. J. Frankl. Inst. 355, 1394–1410 (2018)MathSciNetCrossRefGoogle Scholar
  32. 32.
    Xu, C., Yang, X., Lu, J., Feng, J., Fuad, E., Tasawar, H.: Finite-time synchronization of networks via quantized intermittent pinning control. IEEE Trans. Cybern. 48, 3021–3027 (2018)CrossRefGoogle Scholar
  33. 33.
    Zhang, W., Yang, X., Xu, C., Feng, J., Li, C.: Finite-time synchronization of discontinuous neural networks with delays and mismatched parameters. IEEE Trans. Neural Netw. Learn. Syst. 29, 3761–3771 (2018)MathSciNetCrossRefGoogle Scholar
  34. 34.
    Dai, D., Ma, X.: Chaos synchronization by using intermittent parametric adaptive control method. Phys. Lett. A 288, 23 (2001)CrossRefGoogle Scholar
  35. 35.
    Hu, C., Yu, J., Jiang, H., Teng, Z.: Exponential stabilization and synchronization of neural network swith time-varying delays viaperiodically intermittent control. Nonlinearity 23, 2369 (2010)MathSciNetCrossRefGoogle Scholar
  36. 36.
    Yu, J., Hu, C., Jiang, H., Teng, Z.: Exponential synchronization of Cohen–Grossberg neural networks via periodically intermittent control. Neurocomputing 74, 1776–1782 (2011)CrossRefGoogle Scholar
  37. 37.
    Yang, X., Yang, Z.: Synchronization of TS fuzzy complex dynamical networks with time-varying impulsive delays and stochastic effects. Fuzzy Sets Syst. 235, 25–43 (2014)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature India Private Limited 2019

Authors and Affiliations

  • Chaolong Zhang
    • 1
  • Feiqi Deng
    • 2
    Email author
  • Xisheng Dai
    • 3
  • Shixian Luo
    • 2
  1. 1.College of Computational ScienceZhongkai University of Agriculture and EngineeringGuangzhouPeople’s Republic of China
  2. 2.School of Automation Science and EngineeringSouth China University of TechnologyGuangzhouPeople’s Republic of China
  3. 3.School of Electrical and Information EngineeringGuangxi University of Science and TechnologyLiuzhouPeople’s Republic of China

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