A Novel Three Dimension Autonomous Chaotic System with a Quadratic Exponential Nonlinear Term
Abstract
A novel three dimension autonomous (3D) chaotic system with a quadratic exponential nonlinear term and a quadratic cross-product term is described in this paper. The basic dynamical properties of the new attractor are studied. The forming mechanism of its compound structure, obtained by merging together two simple attractors after performing one mirror operation, has been investigated by detailed numerical as well as theoretical analysis. Finally, the exponential operation circuit and its temperature-compensation circuit, which makes the new system more applicable from a practical engineering perspective, are investigated.
Keywords:
3D chaotic system, exponential nonlinear term, exponential operation circuit, temperature-compensation circuitDownloads
References
E. N. Lorenz, “Deterministic non-periodic flow”, J. Atmos. Sci., Vol. 20, No. 1, pp. 130-141, 1963 DOI: https://doi.org/10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2
O. E . Rossler, “An equation for continuous chaos”, Phys. Lett. A, Vol. 57, No. 5, pp. 397-399, 1976 DOI: https://doi.org/10.1016/0375-9601(76)90101-8
G. Chen, T. Ueta, “Yet another chaotic attractor”, Internat. J. Bifur. Chaos, Vol. 9, No. 7, pp. 1465-1457, 1999 DOI: https://doi.org/10.1142/S0218127499001024
J. Lü, G. Chen, “A new chaotic attractor conined”, Internat. J. Bifur. Chaos, Vol. 12, No. 3, pp. 659-662, 2002 DOI: https://doi.org/10.1142/S0218127402004620
C. Liu, T. Liu, L. Liu, K. Liu, “A new chaotic attractor”, Chaos, Solitons Fractals, Vol. 22, No. 5, pp. 1031-1038, 2004 DOI: https://doi.org/10.1016/j.chaos.2004.02.060
S. Celikovsky, G. Chen, “On the generalized Lorenz canonical form”, Chaos, Solitons Fractals, Vol. 26, No. 5, pp. 1271-1276, 2005 DOI: https://doi.org/10.1016/j.chaos.2005.02.040
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 DOI: https://doi.org/10.1016/j.nonrwa.2010.05.038
W. Zhou, Y. Xu, H. Lu, L. Pan, “On dynamics analysis of a new chaotic attractor”, Phys. Lett. A, Vol. 372, No. 36, pp. 5773-5777, 2008 DOI: https://doi.org/10.1016/j.physleta.2008.07.032
D. Sara, R. M. Hamid, “A novel three-dimensional autonomous chaotic system generating two, three and four-scroll attractors,” Phys. Lett. A, Vol. 373, No. 40, pp. 3637-3642, 2009 DOI: https://doi.org/10.1016/j.physleta.2009.07.088
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