Skip to main content
SpringerLink
Log in

Complex function projective synchronization of general networked chaotic systems by using complex adaptive fuzzy logic

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

Abstract

This paper is concerned with the problem of complex function projective synchronization for uncertain networked chaotic complex systems. Based on Lyapunov stability, an adaptive control method is proposed for complex modified projective synchronization, which guarantees that the general drive-response networked chaotic complex systems are synchronized up to a complex scaling function matrix. Moreover, a complex fuzzy logic-based observer is designed to compensate for the model uncertainties and the external disturbances that exist in response networks, without prior information about uncertain factors. Numerical simulations are presented to demonstrate the effectiveness of the proposed method.

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

Similar content being viewed by others

References

  1. Zhou, J., Lu, J.A., Lü, J.: Adaptive synchronization of an uncertain complex dynamical network. IEEE Trans. Autom. Contr 51, 652–656 (2006)

    Article  Google Scholar 

  2. Li, X., Chen, G.: Synchronization and desynchronization of complex dynamical networks: an engineering viewpoint. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 50, 1381–1390 (2003)

    Article  Google Scholar 

  3. Lü, J., Yu, X., Chen, G.: Chaos synchronization of general complex dynamical networks. Phys. A 334(1–2), 281–302 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  4. Dai, H., Si, G., Zhang, Y.: Adaptive generalized function matrix projective lag synchronization of uncertain complex dynamical networks with different dimensions. Nonlinear Dyn. 74, 629–648 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  5. Mei, J., Jiang, M., Xu, W., Wang, B.: Finite-time synchronization control of complex dynamical networks with time delay. Commun. Nonlinear Sci. Numer. Simul. 18, 2462–2478 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  6. Jia, Z., Fu, X., Deng, G., Li, K.: Group synchronization in complex dynamical networks with different types of oscillators and adaptive coupling schemes. Commun. Nonlinear Sci. Numer. Simul. 18, 2752–2760 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  7. Asheghan, M., Míguez, J.: Robust global synchronization of two complex dynamical networks. Chaos 23, 023108 (2013)

  8. Xu, D., Gui, W., Zhao, P., Yang, C.: Hybrid synchronization of general T-S fuzzy complex dynamical networks with time-varying delay. Math. Probl. Eng. 384654 (2013)

  9. Zheng, S., Shao, W.: Mixed outer synchronization of dynamical networks with nonidentical nodes and output coupling. Nonlinear Dyn. 73, 2343–2352 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  10. Zeng, X., Hui, Q., Haddad, W.M., Hayakawa, T., Bailey, J.M.: Synchronization of biological neural network systems with stochastic perturbations and time delays. J. Frankl. Inst. 351, 1205–1225 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  11. Wang, H., Han, Z., Zhang, W., Xie, Q.: Chaotic synchronization and secure communication based on descriptor observer. Nonlinear Dyn. 57, 69–73 (2009)

    Article  MathSciNet  Google Scholar 

  12. Li, C., Xiong, J., Li, W., Tong, Y., Zeng, Y.: Robust synchronization for a class of fractional-order dynamical system via linear state variable. Indian J. Phys. 87, 673–678 (2013)

    Article  Google Scholar 

  13. Li, C., Su, K., W, L.: Adaptive sliding mode control for synchronization of a fractional-order chaotic system. J. Comput. Nonlinear Dyn. 8, 031005–031011 (2013)

    Article  Google Scholar 

  14. Li, C., Tong, Y., Li, H., Su, K.: Adaptive impulsive synchronization of a class of chaotic and hyperchaotic systems. Phys. Scr. 86, 055003 (2012)

    Article  Google Scholar 

  15. Li, C.: Tracking control and generalized projective synchronization of a class of hyperchaotic system with unknown parameter and disturbance. Commun. Nonlinear Sci. Numer. Simul. 17, 405–413 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  16. He, G., Yang, J.: Adaptive synchronization in nonlinearly coupled dynamical networks. Chaos Solitons Fractals 38, 1254–1259 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  17. Chen, L., Lu, J.: Cluster synchronization in a complex dynamical network with two nonidentical clusters. J. Syst. Sci. Complex 21, 20–33 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  18. Ning, D., Wu, X., Lu, J.A., Feng, H.: Generalized outer synchronization between complex networks with unknown parameters. Abstr. Appl. Anal. 802859 (2013)

  19. Rulkov, N.F., Sushchik, M.M., Tsimring, L.S., Abarbanel, H.D.I.: Generalized synchronization of chaos in directionally coupled chaotic systems. Phys. Rev. E 51, 980–994 (1995)

    Article  Google Scholar 

  20. Zheng, S.: Adaptive-impulsive projective synchronization of drive-response delayed complex dynamical networks with time-varying coupling. Nonlinear Dyn. 67, 2621–2630 (2012)

    Article  MATH  Google Scholar 

  21. Sun, M., Zeng, C.Y., Tian, L.X.: Generalized projective synchronization between two complex networks with time-varying coupling delay. Chin. Phys. Lett. 26, 010501 (2009)

  22. Wei, Q., Wang, X.Y., Hu, X.P.: Hybrid function projective synchronization in complex dynamical networks. AIP Adv. 4, 027128 (2014)

  23. Ricci, F., Tonelli, R., Huang, L., Lai, Y.C.: Onset of chaotic phase synchronization in complex networks of coupled heterogeneous oscillators. Phys. Rev. E 86, 027201 (2012)

    Article  Google Scholar 

  24. Liu, P., Liu, S., Li, X.: Adaptive modified function projective synchronization of general uncertain chaotic complex systems. Phys. Scr. 85, 035005 (2012)

  25. Mahmoud, G.M., Bountis, T., Mahmoud, E.E.: Active control and global synchronization of the complex Chen and Lü systems. Int. J. Bifurc. Chaos 17, 4295–4308 (2007)

  26. Fowler, A.C., Gibbon, J.D., McGuinness, M.J.: The complex Lorenz equations. Physica D 4, 139–163 (1982)

    Article  MathSciNet  Google Scholar 

  27. Wu, Z., Ye, Q., Liu, D.: Finite-time synchronization of dynamical networks coupled with complex-variable chaotic systems. Int. J. Mod. Phys. C 24, 1350058 (2013)

  28. Wu, Z., Chen, G., Fu, X.: Synchronization of a network coupled with complex-variable chaotic systems. Chaos 22, 023127 (2012)

  29. Nian, F., Wang, X., Zheng, P.: Projective synchronization in chaotic complex system with time delay. Int. J. Mod. Phys. B 27, 1350111 (2013)

  30. Mahmoud, G.M., Ahmed, M.E.: Modified projective synchronization and control of complex Chen and Lü systems. J. Vib. Control 17, 1184–1194 (2010)

  31. Hu, M., Yang, Y., Xu, Z., Guo, L.: Hybrid projective synchronization in a chaotic complex nonlinear system. Math. Comput. Simul. 79, 449–457 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  32. Mahmoud, E.E.: Modified projective phase synchronization of chaotic complex nonlinear systems. Math. Comput. Simul. 89, 69–85 (2013)

    Article  Google Scholar 

  33. Wu, Z., Fu, X.: Complex projective synchronization in drive-response networks coupled with complex-variable chaotic systems. Nonlinear Dyn. 72, 9–15 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  34. Wu, Z., Duan, J., Fu, X.: Complex projective synchronization in coupled chaotic complex dynamical systems. Nonlinear Dyn. 69, 771–779 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  35. Liu, S., Zhang, F.: Complex function projective synchronization of complex chaotic system and its applications in secure communication. Nonlinear Dyn. 76, 1087–1097 (2014)

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  37. Wu, X., Wang, J.: Adaptive generalized function projective synchronization of uncertain chaotic complex systems. Nonlinear Dyn. 73, 1455–1467 (2013)

    Article  Google Scholar 

  38. Luo, C., Wang, X.: Hybrid modified function projective synchronization of two different dimensional complex nonlinear systems with parameters identification. J. Frankl. Inst. 350, 2646–2663 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  39. Mahmoud, G.M., Mahmoud, E.E.: Modified projective lag synchronization of two nonidentical hyperchaotic complex nonlinear systems. Int. J. Bifurc. Chaos 21, 2369–2379 (2011)

    Article  Google Scholar 

  40. Zheng, S.: Parameter identification and adaptive impulsive synchronization of uncertain complex-variable chaotic systems. Nonlinear Dyn. 74, 957–967 (2013)

    Article  MATH  Google Scholar 

  41. Liu, S., Liu, P.: Adaptive anti-synchronization of chaotic complex nonlinear systems with unknown parameters. Nonlinear Anal. Real World Appl. 12, 3046–3055 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  42. Liu, P., Liu, S.: Robust adaptive full state hybrid synchronization of chaotic complex systems with unknown parameters and external disturbances. Nonlinear Dyn. 70, 585–599 (2012)

    Article  Google Scholar 

  43. Wu, T.S., Karkoub, M.: \(\text{ H }_{\infty }\) fuzzy adaptive tracking control design for nonlinear systems with output delays. Fuzzy Set Syst. (2014)

  44. Jeong, S.C., Ji, D.H., Park, J.H., Won, S.C.: Adaptive synchronization for uncertain complex dynamical network using fuzzy disturbance observer. Nonlinear Dyn. 71, 223–234 (2013)

    Article  MathSciNet  Google Scholar 

  45. Zhou, A.T., Tang, Y., Chen, G.: Complex dynamical behaviors of the chaotic Chen’s system. Int. J. Bifurc. Chaos 13, 2561–2574 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  46. Buckley, J.J.: Fuzzy complex numbers. Fuzzy Set Syst. 33, 333–345 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  47. Buckley, J.J., Qu, Y.: Fuzzy complex analysis I: differentiation. Fuzzy Set Syst. 41, 269–284 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  48. Slotine, J.J.E., Li, W.: Applied Nonlinear Control. Prentice Hall, Englewood Cliffs (1991)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electronic and Electrical Engineering, POSTECH, San 31 Hyoja-Dong, Pohang, 790-784, Republic of Korea

    J. W. Lee & S. C. Won

  2. Department of Electronic Engineering, Daegu University, Gyungsan, 712-714, Republic of Korea

    S. M. Lee

Authors
  1. J. W. Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. M. Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. C. Won
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. C. Won.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lee, J.W., Lee, S.M. & Won, S.C. Complex function projective synchronization of general networked chaotic systems by using complex adaptive fuzzy logic. Nonlinear Dyn 81, 2095–2106 (2015). https://doi.org/10.1007/s11071-015-2128-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-015-2128-8

Keywords

Search

Navigation