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

详细信息    查看全文

• 作者：Chunbiao Li (123) goontry@126.com
  Jun Wang (3)
  Wen Hu (4)
• 关键词：Absolute term – ; Constant Lyapunov exponent spectrum – ; Chaotic attractor
• 刊名：Nonlinear Dynamics
• 出版年：2012
• 出版时间：June 2012
• 年：2012
• 卷：68
• 期：4
• 页码：575-587
• 全文大小：4.4 MB
• 参考文献：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)
  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)
  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)
  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)
  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)
  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)
  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)
  8. Hu, M., Yang, Y., Xu, Z.: Impulsive control of projective synchronization on chaotic systems. Phys. Lett. A 372, 3228–3233 (2008)
  9. Yu, Y.: Adaptive synchronization of a unified chaotic system. Chaos Solitons Fractals 36, 329–333 (2008)
  10. Cao, J., Lu, J.: Adaptive synchronization of neural networks with or without time-varying delay. Chaos 16, 013133 (2006)
  11. Yan, Z.: A new scheme to generalized (lag, anticipated, and complete) synchronization in chaotic and hyperchaotic systems. Chaos 15, 013101 (2005)
  12. Lu, J., Wu, X., L眉, J.: Synchronization of a unified chaotic system and the application in secure communication. Phys. Lett. A 305, 365–370 (2002)
  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)
  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)
  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)
  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)
• 作者单位：1. School of Information Science and Engineering, Southeast University, Nanjing, 210096 China2. Department of Mechanical and Electrical Engineering, Jiangsu Institute of Economic and Trade Technology, Nanjing, 210007 China3. Engineering Technology Research and Development Center of Jiangsu Circulation Modernization Sensor Network, Jiangsu Institute of Economic and Trade Technology, Nanjing, 210007 China4. College of Electronic and Information Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016 China
• 刊物类别：Engineering
• 刊物主题：Vibration, Dynamical Systems and Control
  Mechanics
  Mechanical Engineering
  Automotive and Aerospace Engineering and Traffic
  
• 出版者：Springer Netherlands
• ISSN：1573-269X

文摘

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.