A Novel Three Dimension Autonomous Chaotic System with a Quadratic Exponential Nonlinear Term
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 circuit
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
How to Cite
MetricsAbstract Views: 729
PDF Downloads: 396
Authors who publish with this journal agree to the following terms:
- Authors retain the copyright and grant the journal the right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) after its publication in ETASR with an acknowledgement of its initial publication in this journal.