Skip to main content
SpringerLink
Log in

A New Chaotic Attractor and Its Synchronization Implementation

  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

Abstract

A new three-dimensional autonomous chaotic system is proposed in this paper. It analyzes dynamic behaviors of this new system, including the stability of equilibria, the system dissipativity, poincare maps, Lyapunov exponent, bifurcation, wave forms, and spectrum. Numeral simulation is performed in Matlab. A chaotic circuit is designed, and the corresponding circuit simulation is conducted. The results show that the chaotic attractor exists in the new system. The synchronization problem of the chaotic system is solved with a synchronization method, and its synchronization circuit is designed. Numeral simulation and circuit simulation show that the synchronization problem of this chaotic system proposed is solved.

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
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20

Similar content being viewed by others

References

  1. S. Celikovsky, G.R. Chen, On a generalized Lorenz canonical form of chaotic systems. Int. J. Bifur. Chaos 12(8), 1789–1812 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  2. G.R. Chen, T. Ueta, Yet another chaotic attractor. Int. J. Bifur. Chaos 9(7), 1465–1466 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  3. G.R. Chen, J.H. Lü, Analysis, Control and Synchronization of Generalized Lorenz System (Science press, Beijing, 2003)

    Google Scholar 

  4. Y. Chen, M.Y. Li, Z.F. Cheng, Global anti-synchronization of master-slave chaotic modified Chua’s circuits coupled by linear feedback control. Math. Comput. Model. 52, 567–573 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  5. L.O. Chua, M. Komuro, T. Matsumoto, The double scroll family. IEEE Trans. Circuits Syst. 33(11), 1072–1118 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  6. K.M. Cuomo, A.V. Oppenheim, Circuit implementation of synchronized chaos with applications to communications. Phys. Rev. Lett. 71(1), 65–68 (1993)

    Article  Google Scholar 

  7. L.G. de la Fraga, E. Tlelo-Cuautle, Optimizing the maximum lyapunov exponent and phase space portraits in multi-scroll chaotic oscillators. Nonlinear Dyn. 76(2), 1503–1515 (2014)

    Article  Google Scholar 

  8. A.S. Hegazi, H.N. Agiza, M.M. El-Dessoky, Adaptive synchronization for Rössler and Chua’s circuit systems. Int. J. Bifur. Chaos 12(7), 1579–1597 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  9. M. Itoh, C.W. Wu, L.O. Chua, Communication systems via chaotic signals from a reconstruction viewpoint. Int. J. Bifur. Chaos 7(2), 275–286 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  10. K. Klomkarn, P. Sooraksa, G.R. Chen, New construction of mixed-mode chaotic circuits. Int. J. Bifur. Chaos 20(5), 1485–1497 (2010)

    Article  Google Scholar 

  11. L. Kocarev, U. Parlitz, General approach for chaotic synchronization with applications to communications. Phys. Rev. Lett. 74, 5028–5031 (1995)

    Article  Google Scholar 

  12. X.F. Li, Y.D. Chu, J.G. Zhang, Y.X. Chang, Nonlinear dynamics and circuit implementation for a new Lorenz-like attractor. Chaos. Chaos Solit. Fract. 41, 2360–2370 (2009)

    Article  MATH  Google Scholar 

  13. T.L. Liao, S.H. Lin, Adaptive control and synchronization of Lorenz systems. J. Frankl. Inst. 336, 925–937 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  14. T.L. Liao, S.H. Tsai, Adaptive synchronization of chaotic systems and its application to secure communications. Chaos Solit. Fract. 11, 1387–1396 (2000)

    Article  MATH  Google Scholar 

  15. C.X. Liu, T. Liu, L. Liu, K. Liu, A new chaotic attractor. Chaos Solit. Fract. 22, 1031–1038 (2004)

    Article  MATH  Google Scholar 

  16. E.N. Lorenz, Deterministic nonperiodic flow. J. Atmos. Sci. 20, 130–141 (1963)

    Article  Google Scholar 

  17. J.A. Lu, X.Q. Wu, X.P. Han, J.H. Lü, adaptive feedback synchronization of a unified chaotic system. Phys. Lett. A 329, 327–333 (2004)

    Article  MATH  Google Scholar 

  18. J.H. Lü, G.R. Chen, A new chaotic attractor coined. Int. J. Bifur. Chaos 12(3), 659–661 (2002)

    Article  MATH  Google Scholar 

  19. J.H. Lü, G.R. Chen, D.Z. Cheng, S. Celikovsky, Bridge the gap between the Lorenz system and the chen system. Int. J. Bifur. Chaos 12(12), 2917–2926 (2002)

    Article  MATH  Google Scholar 

  20. J.M. Munoz-Pacheco, E. Zambrano-Serrano, O. Felix-Beltran, Synchronization of PWL function-based 2D and 3D multi-scroll chaotic systems. Nonlinear Dyn. 70, 1633–1643 (2012)

    Article  MathSciNet  Google Scholar 

  21. R.W. Newcomb, N. El-Leithy, Chaos generation using binary hysteresis. Circuit Syst. Sig. Process. 5(3), 321–341 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  22. E. Ortega-Torres, C. Sanchez-Lopez, J. Mendoza-Lopez, Frequency behavior of saturated nonlinear function series based on opamps. Rev. Mex. Fis. 59, 504–510 (2013)

    MathSciNet  Google Scholar 

  23. E. Ott, C. Grebogi, J.A. Yorke, Controlling Chaos. Phys. Rev. Lett. 64, 1196–1199 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  24. S. Ozoguz, A.S. Elwakil, M.P. Kennedy, Experimental verification of the butterfly attractor in a modified Lorenz system. Int. J. Bifur. Chaos 12(7), 1627–1632 (2002)

    Article  Google Scholar 

  25. O.E. Rössler, An equation for continuous chaos. Phys. Lett. A 57(5), 397–398 (1976)

    Article  Google Scholar 

  26. T. Saito, An approach toward higher dimensional hysteresis Chaos genearators. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 37(3), 399–409 (1990)

    Article  MATH  Google Scholar 

  27. C. Sanchez-Lopez, R. Trejo-Guerra, J.M. Munoz-Pacheco, N-scroll chaotic attractors from saturated function series employing CCII+s. Nonlinear Dyn. 61, 331–341 (2010)

    Article  MATH  Google Scholar 

  28. V. Sundarapandian, I. Pehlivan, Analysis, control, synchronization, and circuit design of a novel chaotic system. Math. Comput. Model. 55, 1904–1915 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  29. R. Trejo-Guerra, E. Tlelo-Cuautle, C. Cruz-Hernandez, Chaotic communication system using chua’s oscillators realized with CCII+s. Int. J. Bifurc. Chaos 19(17), 4217–4226 (2009)

    Article  Google Scholar 

  30. R. Trejo-Guerra, E. Tlelo-Cuautle, C. Sanchez-Lopez, Realization of multiscroll chaotic attractors by using current-feedback operational amplifiers. Rev. Mex. Fis. 56(4), 268–274 (2010)

    Google Scholar 

  31. R. Trejo-Guerra, E. Tlelo-Cuautle, M. Jimenez-Fuentes, Integrated circuit generating 3-and 5-scroll attractors. Commun Nonlinear Sci. Numer. Simul. 17, 4328–4335 (2012)

    Article  MathSciNet  Google Scholar 

  32. R. Trejo-Guerra, E. Tlelo-Cuautle, M. Jimenez-Fuentes, Multiscroll floating gate-based integrated chaotic oscillator. Int. J. Circ. Theor. Appl. 41, 831–843 (2013)

    Article  Google Scholar 

  33. A. Vanecek, S. Celikovsky, Control Systems: From Linear Analysis to Synthesis of Chaos (Prentice-hall, London, 1996)

    MATH  Google Scholar 

  34. Y.W. Wang, Z.H. Guan, H.O. Wang, Feedback and adaptive control for the synchronization of Chen system via a single variable. Phys. Lett. A 312, 34–40 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  35. F.Q. Wang, C.X. Liu, Synchronization of Liu chaotic system based on linear feedback control and its experimental verification. Acta Phys. Sin. 55(10), 5055–5060 (2006)

    Google Scholar 

  36. X.Y. Wang, Q.L. Zhu, X.P. Zhang, Synchronization of new Lü chaotic system via three methods. Acta Phys. Sin. 60(10), 100510-1-9 (2011)

    MathSciNet  Google Scholar 

  37. X.H. Yu, Controlling Lorenz chaos. Int. J. Syst. Sci. 27(4), 355–359 (1996)

    Article  MATH  Google Scholar 

  38. C.X. Zhang, S.M. Yu, G.R. Chen, Design and implementation of compound chaotic attractors. Int. J. Bifur. Chaos 22(5), 1250120 (2012)

    Article  Google Scholar 

Download references

Acknowledgments

The work was supported by the National Natural Science Foundation for Distinguished Young Scholars of China (Grant No. 50925727), the Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 51107034), The National Defense Advanced Research Project, China (Grant No. C1120110004, 9140A27020211DZ5102), the Foundation for Key Program of Ministry of Education, China (Grant No. 313018), and the Natural Science Foundation of Hunan Province, China (Grant Nos. 2011J4, 2011JK2023, 12JJA004).

Author information

Authors and Affiliations

  1. College of Electrical and Information Engineering, Hunan University, Changsha, 410082, People’s Republic of China

    Xianming Wu & Wenxin Yu

  2. School of Electrical and Automation Engineering, Hefei University of Technology, Hefei, 230009, People’s Republic of China

    Yigang He & Baiqiang Yin

Authors
  1. Xianming Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yigang He
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Wenxin Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Baiqiang Yin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xianming Wu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wu, X., He, Y., Yu, W. et al. A New Chaotic Attractor and Its Synchronization Implementation. Circuits Syst Signal Process 34, 1747–1768 (2015). https://doi.org/10.1007/s00034-014-9946-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-014-9946-7

Keywords

Search

Navigation