Skip to main content

Transmission Synchronization Control of Multiple Non-identical Coupled Chaotic Systems

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9719))

Abstract

In this paper, we investigate the transmission projective synchronization control problem for multiple, non-identical, coupled chaotic systems. By considering the influence of the occurrence of a fault between a driving system and a responding system, we define our new transmission synchronization scheme. After that, control laws are designed to achieve transmission projective synchronization and a simple stability criteria is obtained for reaching the transmission synchronization among multi-systems. A numerical example is used to verify the effectiveness of the synchronization within a desired scaling factor.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

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

    Article  MathSciNet  MATH  Google Scholar 

  2. Sun, J., Shen, Y., Zhang, G.D., et al.: Combination-combination synchronization among four identical or different chaotic systems. Nonlinear Dyn. 73, 1211–1222 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  3. Jiang, C.M., Liu, S.T.: Generalized combination complex synchronization of new hyperchaotic complex Lü-like systems. Adv. Differ. Equ. 214, 1–17 (2015)

    MathSciNet  Google Scholar 

  4. Chen, X.Y., Qiu, J.L., Cao, J.D., He, H.B.: Hybrid synchronization behavior in an array of coupled chaotic systems with ring connection. Neurocomputing 173, 1299–1309 (2016)

    Article  Google Scholar 

  5. Bhowmick, S.K., Ghosh, D.: Targeting engineering synchronization in chaotic systems. Int. J. Mod. Phys. C 27, 1650006 (2016)

    Google Scholar 

  6. Sun, J., Shen, Y., Yin, Q., Xu, C.J.: Compound synchronization of four memristor chaotic oscillator systems and secure communication. Chaos 23, 013140 (2013)

    Google Scholar 

  7. Sun, J., Shen, Y., Zhang, G.D.: Transmission projective synchronization of multi-systems with non-delayed and delayed coupling via impulsive control. Chaos 22, 043107 (2012)

    Google Scholar 

  8. Chen, X.Y., Qiu, J.L., Song, Q., Zhang, A.C.: Synchronization of N coupled chaotic systems with ring connection based on special antisymmetric structure. Abstr. Appl. Anal. 2013, 680604 (2013)

    Google Scholar 

  9. Chen, X.Y., Wang, C.Y., Qiu, J.L.: Synchronization and anti-synchronization of N different coupled chaotic systems with ring connection. Int. J. Mod. Phys. C 25, 1–12 (2014)

    Google Scholar 

  10. Gong, H.C., Chen, X.Y., Qiu, J.L., et al.: Generalized projective synchronization of an array of non-identical coupled chaotic systems. In: The 26th Chinese Control and Decision Conference, pp. 119–123. IEEE Press, New York (2014)

    Google Scholar 

  11. Yu, Y., Zhang, S.: Global synchronization of three coupled chaotic systems with ring connection. Chaos Solitions Fractals 24, 1233–1242 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  12. Liu, Y., Lü, L.: Synchronization of N different coupled chaotic systems with ring and chain connections. Appl. Math. Mech. 29, 1181–1190 (2008)

    MathSciNet  Google Scholar 

  13. Tang, Y., Fang, J.A.: Synchronization of N-coupled Fractional-order chaotic systems with ring connection. Commun. Nonlinear Sci. Numer. Simul. 15, 401–412 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  14. Yang, L., Zhang, J.: Synchronization of three identical systems and its application for secure communication with noise perturbation. In: International Conference on Information Engineering and Computer Science, pp. 1–4. IEEE Press, New York (2009)

    Google Scholar 

  15. Cheng, L.Y., Chen, X.Y., Qiu, J.L., et al.: Transmission projective synchronization in an array of identical coupled chaotic systems. In: The 33th Chinese Control Conference, pp. 2789–2793. IEEE Press, New York (2014)

    Google Scholar 

  16. Cai, N., Jing, Y.W., Zhang, S.Y.: Generalized projective synchronization of different chaotic systems based on antisymmetric structure. Chaos Solitons Fractals 42, 1190–1196 (2009)

    Article  MATH  Google Scholar 

  17. Liu, B., Zhang, K.: Stability of nonlinear systems with tridiagonal structure and its applications. Acta Autom. Sin. 33, 442–446 (2007)

    MathSciNet  Google Scholar 

Download references

Acknowledgement

This work was supported in part by the Applied Mathematics Enhancement Program (AMEP) of Linyi University and the National Natural Science Foundation of China (No.61403179, 61273012), by a Project of the Postdoctoral Sustentation Fund of Jiangsu Province under Grant 1402042B.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jianlong Qiu .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Chen, X., Cao, J., Qiu, J., Yang, C. (2016). Transmission Synchronization Control of Multiple Non-identical Coupled Chaotic Systems. In: Cheng, L., Liu, Q., Ronzhin, A. (eds) Advances in Neural Networks – ISNN 2016. ISNN 2016. Lecture Notes in Computer Science(), vol 9719. Springer, Cham. https://doi.org/10.1007/978-3-319-40663-3_33

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-40663-3_33

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-40662-6

  • Online ISBN: 978-3-319-40663-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics