A New Chaotic Attractor with Quadratic Exponential Nonlinear Term from Chen's Attractor

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Iftikhar Ahmed
Chunlai Mu
Fuchen Zhang


In this paper a new three-dimensional chaotic system is proposed, which relies on a nonlinear exponential term and a nonlinear quadratic cross term necessary for folding trajectories. Basic dynamical characteristics of the new system are analyzed. Compared with the Chen system, the equilibrium points of the new system does not contain the origin, and has a greater positive Lyapunov index, can produce more complex shaped chaotic attractor.

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  1. E. N. Lorenz, Deterministic non-periodic flow? J.Atmos. Sci., Vol. 20, No. 1, pp. 130-141, 1963.
  2. O. E . Rossler, An equation for continuous chaos?Phys. Lett. A, Vol. 57, No. 5, pp. 397-399, 1976.
  3. G. Chen, T. Ueta, Yet another chaotic attractor? Internat. J. Bifur. Chaos, Vol. 9, No. 7, pp. 1465-1457, 1999.
  4. J. L? G. Chen, A new chaotic attractor conined? Internat. J. Bifur. Chaos, Vol. 12, No. 3, pp. 659-662, 2002.
  5. C. Liu, T. Liu, L. Liu, K. Liu, A new chaotic attractor? Chaos, Solitons Fractals, Vol. 22, No. 5, pp. 1031-1038, 2004.
  6. S. Celikovsky, G. Chen, On the generalized Lorenz canonical form? Chaos, Solitons Fractals, Vol. 26, No. 5, pp. 1271-1276, 2005.
  7. Z. Wei, Q. Yang, Dynamical analysis of a new autonomous 3-D chaotic system only with stable equilibria? Nonlinear Anal.: RWA, Vol. 12, No. 1, pp. 106-118, 2011.
  8. Z.Liang, W. Zhonglin, ”Design and realization of a new chaotic system”, Sensor Netw. Sec. Technol. and Prc. Commun. Syst., 2013 International Conference on, 10.1109/SNS-PCS.2013.6553844, pp.101-104, 2013.
  9. Li, X.F., Chlouverakis, K.E., Xu, D.L.: Nonlinear dynamics and circuit realization of a new chaotic flow: A variant of Lorenz, Chen and Lu. Nonlinear Anal. 10, 2357-2368 (2009) .
  10. Hahn, W., The Stability of Motion. Springer, New York (1967).