Skip to main content
SpringerLink
Log in

Finite-time synchronization of nonidentical chaotic systems with multiple time-varying delays and bounded perturbations

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

This paper is concerned with synchronization in a setting time for drive-response chaotic systems with multiple time-varying delays. The driving and response systems exhibit different dynamical behaviors with nonidentical delays and uncertain bounded external perturbations. Due to the time delays, existing finite-time stability theorem cannot be applied to the synchronization goal. By designing suitable controller and designing some Lyapunov–Krasovskii functionals, sufficient conditions guaranteeing the finite-time synchronization are derived without using existing finite-time stability theorem. Results of this paper extend most of existing ones which can only finite-timely synchronize coupled identical systems without delay. Numerical simulations demonstrate the effectiveness of the theoretical analysis.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. Pecora, L., Carroll, T.: Synchronization in chaotic systems. Phys. Rev. Lett. 64(8), 821–824 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  2. Park, H.: Chaos synchronization between two different chaotic dynamical systems. Chaos Solitons Fractals 27(2), 549–554 (2006)

    Article  MATH  Google Scholar 

  3. Bowong, S., Kakmeni, F.M., Fotsin, H.: A new adaptive observer-based synchronization scheme for private communication. Phys. Lett. A 355(3), 193–201 (2006)

    Article  Google Scholar 

  4. Jiang, G., Chen, G., Tang, K.: A new criterion for chaos synchronizaton using linear state feedback control. Int. J. Bifurc. Chaos 13(8), 2343–2351 (2003)

    Article  MATH  Google Scholar 

  5. Huang, T., Li, C., Yu, W., Chen, G.: Synchronization of delayed chaotic systems with parameter mismatches by using intermittent linear state feedback. Nonlinearity 22(3), 569–584 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  6. Ma, J., Song, X., Jin, W., Wang, C.: Autapse-induced synchronization in a coupled neuronal network. Chaos Solitons Fractals 80, 31–38 (2015)

    Article  MathSciNet  Google Scholar 

  7. Yang, X., Cao, J.: Exponential synchronization of delayed neural networks with discontinuous activations. IEEE Trans. Circuits Syst. I 60(9), 2431–2439 (2013)

    Article  MathSciNet  Google Scholar 

  8. Mahmoud, G.M., Mahmoud, E.E.: Complete synchronization of chaotic complex nonlinear systems with uncertain parameters. Nonlin. Dyn. 62(4), 875–882 (2010)

    Article  MATH  Google Scholar 

  9. Zhang, R., Yang, S.: Adaptive synchronization of fractional-order chaotic systems via a single driving variable. Nonlin. Dyn. 66(4), 831–837 (2011)

    Article  MATH  Google Scholar 

  10. Yang, X., Wu, Z., Cao, J.: Finite-time synchronization of complex networks with nonidentical discontinuous nodes. Nonlin. Dyn. 73(4), 2313–2327 (2010)

    Article  MathSciNet  Google Scholar 

  11. Cortes, J.: Finite-time convergent gradient flows with applications to network consensus. Automatica 42(11), 1993–2000 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  12. Hui, Q., Haddad, W.M., Bha, S.P.: Finite-time semistability and consensus for nonlinear dynamical networks. IEEE Trans. Autom. Control 53(8), 1887–1900 (2008)

    Article  Google Scholar 

  13. Xiao, F., Wang, L., Chen, J., Gao, Y.: Finite-time formation control for multi-agentsystems. Automatica 45(11), 2605–2611 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  14. Wang, L., Xiao, F.: Finite-time consensus problems for networks of dynamic agents. IEEE Trans. Autom. Control 55(4), 950–955 (2010)

    Article  MathSciNet  Google Scholar 

  15. Aghababa, M.P., Khanmohammadi, S., Alizadeh, G.: Finite-time synchronization of two different chaotic systems with unknown parameters via sliding mode technique. Appl. Math. Modell. 35(6), 3080–3091 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  16. Wang, H., Han, Z., Xie, Q., Zhang, W.: Finite-time synchronization of uncertain unified chaotic systems based on CLF. Nonlin. Anal. Real World Appl. 10(5), 2003–2047 (2009)

    MathSciNet  Google Scholar 

  17. Shen, J., Cao, J.: Finite-time synchronization of coupled neural networks via discontinuous controllers. Cogn. Neurodyn. 5(4), 373–385 (2011)

    Article  MathSciNet  Google Scholar 

  18. Aghababa, M.P., Aghababa, H.P.: Synchronization of mechanical horizontal platform systems in finite time. Appl. Math. Modell. 36(10), 4579–4591 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  19. Qin, H., Ma, J., Jin, W.: Dynamics of electric activities in neuron and neurons of network induced by autapses. Technol. Sci. 57(5), 936–946 (2014)

    MathSciNet  Google Scholar 

  20. Qin, H., Ma, J., Wang, C., Chu, R.: Autapse-induced target wave, spiral wave in regular network of neurons. Sci. China 57(10), 1918–1926 (2014)

    Article  Google Scholar 

  21. Tang, Y.: Terminal sliding mode control for rigid robots. Automatica 34(1), 51–56 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  22. Forti, M., Grazzini, M., Nistri, P., Pancioni, L.: Generalized Lyapunov approach for convergence of neural networks with discontinuous or non-Lipschitz activations. Phys. D 214(1), 88–99 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  23. Efimov, D., Polyakov, A., Fridman, E.: Comments on finite-time stability of time-delay systems. Automatica 50(7), 1944–1947 (2014)

    Article  MATH  MathSciNet  Google Scholar 

  24. Moulay, E., Dambrine, M., Yeganefar, N.: Finite-time stability and stabilization of time-delay systems. Syst. Control Lett. 57(7), 561–566 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  25. Yang, X.: Can neural networks with arbitrary delays befinite-timely synchronized? Neurocomputing 143(2), 275–281 (2014)

    Article  Google Scholar 

  26. Wu, X., Lai, D., Lu, H.: Generalized synchronization of the fractional-order chaos in weighted complex dynamical networks with nonidentical nodes. Nonlin. Dyn. 69(12), 667–683 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  27. Zhao, J., Hill, D.J., Liu, T.: Synchronization of dynamical networks with nonidentical nodes: criteria and control. IEEE Trans. Circuits Syst. I 58(3), 584–594 (2011)

    Article  MathSciNet  Google Scholar 

  28. Lu, W., Liu, B., Chen, T.: Cluster synchronization in networks of coupled nonidentical dynamical systems. Chaos 20(1), 1–12 (2010)

  29. Wu, Z., Fu, X.: Cluster mixed synchronization via pinning control and adaptive coupling strength in community networks with nonidentical nodes. Commun. Nonlin. Sci. Numer. Simul. 17(4), 1628–1636 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  30. Wagg, D.J.: Partial synchronization of nonidentical chaotic systems via adaptive control, with applications to modeling coupled nonlinear systems. Int. J. Bifurc. Chaos 12(3), 561–570 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  31. He, W., Qian, F., Cao, J., Han, Q.: Impulsive synchronization of two nonidentical chaotic systems with time-varying delay. Phy. Lett. A 375(3), 498–504 (2011)

  32. Yang, X., Cao, J., Lu, J.: Stochastic synchronization of complex networks with nonidentical nodes via hybrid adaptive and impulsive control. IEEE Trans. Circuits Syst. I 59(2), 371–384 (2012)

    Article  MathSciNet  Google Scholar 

  33. Yang, X., Zhu, Q., Huang, C.: Lag stochastic synchronization of chaotic mixed time-delayed neural networks with uncertain parameters or pertuibations. Neurocomputing 74(10), 1617–1625 (2011)

    Article  MathSciNet  Google Scholar 

  34. Park, J.H.: Robust guaranteed cost control for uncertain linear differential systems of neutral type. Appl. Math. Comput. 140(2), 523–535 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  35. Wang, B., Shi, P., Karimi, H.R., Song, Y., Wang, J.: Robust \(H_{\infty }\) synchronization of a hyper-chaotic system with disturbance input. Nonlin. Anal. Real World Appl. 14(3), 1487–1495 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  36. Yang, X., Cao, J.: Hybrid adaptive and impulsive synchronization of uncertain complex networks with delays and general uncertain perturbations. Appl. Math. Comput. 227(15), 480–493 (2014)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgments

This work was supported by the National Natural Science Foundation of China (NSFC) under Grant Nos. 61263020 and 11471061, the Natural Science Foundation of Scientific and Technical Committee of Chongqing City under Grant No. cstc2014jcyjA00014, and the Research Foundation of HongHe University under Grant No. XJ15SX05.

Author information

Authors and Affiliations

  1. Department of Mathematics, Honghe University, Mengzi, 661199, China

    Lei Shi, Yingchun Li & Zuzhen Feng

  2. Department of Mathematics, Chongqing Normal University, Chongqing, 401331, China

    Xinsong Yang

Authors
  1. Lei Shi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xinsong Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yingchun Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Zuzhen Feng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xinsong Yang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shi, L., Yang, X., Li, Y. et al. Finite-time synchronization of nonidentical chaotic systems with multiple time-varying delays and bounded perturbations. Nonlinear Dyn 83, 75–87 (2016). https://doi.org/10.1007/s11071-015-2310-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-015-2310-z

Keywords

Search

Navigation