Nonlinear Dynamics

, Volume 68, Issue 4, pp 575–587 | Cite as

Absolute term introduced to rebuild the chaotic attractor with constant Lyapunov exponent spectrum

Original Paper


When positive or negative feedback of absolute terms are introduced in dynamic equations of improved chaotic system with constant Lyapunov exponent spectrum, diverse structures of chaotic attractors can be rebuilt, numbers of novel attractors found and subsequently the dynamical behavior property analyzed. Drawing on the concept of global phase reversal and its implementation methods, three main features are discussed and a systematic conclusion is made, that is, the unique class of chaotic system which utilizes merely absolute terms to realize nonlinear function possesses the following three properties: adjustable amplitude, adjustable phase reversal and constant Lyapunov exponent spectrum.


Absolute term Constant Lyapunov exponent spectrum Chaotic attractor 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Hu, W., Liu, Z., Li, C.B.: Synchronization-based scheme for calculating ambiguity functions of wideband chaotic signals. IEEE Trans. Aerosp. Electron. Syst. 44, 367–372 (2008) CrossRefGoogle Scholar
  2. 2.
    Lee, S.M., Choi, S.J., Ji, D.H., Park, J.H., Won, S.C.: Synchronization for chaotic Lur’e systems with sector-restricted nonlinearities via delayed feedback control. Nonlinear Dyn. 59, 277–288 (2010) MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Gamal, M., Shaban, M., Aly, A., AL-Kashif, M.A.: Dynamical properties and chaos synchronization of a new chaotic complex nonlinear system. Nonlinear Dyn. 51, 171–181 (2008) MATHGoogle Scholar
  4. 4.
    Zhang, L.P., Jiang, H.B., Bi, Q.S.: Reliable impulsive lag synchronization for a class of nonlinear discrete chaotic systems. Nonlinear Dyn. 59, 529–534 (2010) MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    Zhang, R.X. Yang S.P.: Chaos in fractional-order generalized Lorenz system and its synchronization circuit simulation. Chin. Phys. 18, 3295–3303 (2009) CrossRefGoogle Scholar
  6. 6.
    Li, C.B., Wang, D.C.: An attractor with invariable Lyapunov exponent spectrum and its Jerk circuit implementation. Acta Phys. Sin. 58, 570–764 (2009) Google Scholar
  7. 7.
    Li, C.B., Chen, S., Zhu, H.Q.: Circuit implementation and synchronization of an improved system with invariable Lyapunov exponent spectrum. Acta Phys. Sin. 58, 2255–2265 (2009) MATHGoogle Scholar
  8. 8.
    Hu, M., Yang, Y., Xu, Z.: Impulsive control of projective synchronization on chaotic systems. Phys. Lett. A 372, 3228–3233 (2008) MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Yu, Y.: Adaptive synchronization of a unified chaotic system. Chaos Solitons Fractals 36, 329–333 (2008) MATHCrossRefGoogle Scholar
  10. 10.
    Cao, J., Lu, J.: Adaptive synchronization of neural networks with or without time-varying delay. Chaos 16, 013133 (2006) MathSciNetCrossRefGoogle Scholar
  11. 11.
    Yan, Z.: A new scheme to generalized (lag, anticipated, and complete) synchronization in chaotic and hyperchaotic systems. Chaos 15, 013101 (2005) MathSciNetCrossRefGoogle Scholar
  12. 12.
    Lu, J., Wu, X., Lü, J.: Synchronization of a unified chaotic system and the application in secure communication. Phys. Lett. A 305, 365–370 (2002) MathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    Rafikov, M., Balthazar, J.M.: On control and synchronization in chaotic and hyperchaotic systems via linear feedback control. Commun. Nonlinear Sci. Numer. Simul. 13, 1246–1255 (2008) MathSciNetMATHCrossRefGoogle Scholar
  14. 14.
    Cao, J.D., Li, H.X.: Ho, D.W.C.: Synchronization criteria of Lur’e systems with time-delay feedback control. Chaos Solitons Fractals 23, 1285–1298 (2005) MathSciNetMATHGoogle Scholar
  15. 15.
    Li, C.B., Wang, H.K.: An extension system with constant Lyapunov exponent spectrum and its evolvement study. Acta Phys. Sin. 58, 7514–7524 (2009) Google Scholar
  16. 16.
    Li, C.B., Wang, H.K., Chen, S.: A novel chaotic attractor with constant Lyapunov exponent Spectrum and its circuit implementation. Acta Phys. Sin. 59, 783–791 (2010) MathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.School of Information Science and EngineeringSoutheast UniversityNanjingChina
  2. 2.Department of Mechanical and Electrical EngineeringJiangsu Institute of Economic and Trade TechnologyNanjingChina
  3. 3.Engineering Technology Research and Development Center of Jiangsu Circulation Modernization Sensor NetworkJiangsu Institute of Economic and Trade TechnologyNanjingChina
  4. 4.College of Electronic and Information EngineeringNanjing University of Aeronautics and AstronauticsNanjingChina

Personalised recommendations