Generating one-, two-, three- and four-scroll attractors from a novel four-dimensional smooth autonomous chaotic system

doi:10.1088/1674-1056/19/6/060506

中国物理B ›› 2010, Vol. 19 ›› Issue (6): 60506-060506.doi: 10.1088/1674-1056/19/6/060506

Generating one-, two-, three- and four-scroll attractors from a novel four-dimensional smooth autonomous chaotic system

SaraDadras, HamidRezaMomeni

Automation and Instruments Lab, Electrical Engineering Department, Tarbiat Modares University, P.O. Box 14115-143, Tehran, Iran

收稿日期:2009-10-20 出版日期:2010-06-15 发布日期:2010-06-15

Generating one-, two-, three- and four-scroll attractors from a novel four-dimensional smooth autonomous chaotic system

Sara Dadras and Hamid Reza Momeni^†

Automation and Instruments Lab, Electrical Engineering Department, Tarbiat Modares University, P.O. Box 14115-143, Tehran, Iran

Received:2009-10-20 Online:2010-06-15 Published:2010-06-15

摘要/Abstract

摘要： A new four-dimensional quadratic smooth autonomous chaotic system is presented in this paper, which can exhibit periodic orbit and chaos under the conditions on the system parameters. Importantly, the system can generate one-, two-, three- and four-scroll chaotic attractors with appropriate choices of parameters. Interestingly, all the attractors are generated only by changing a single parameter. The dynamic analysis approach in the paper involves time series, phase portraits, Poincar\'{e} maps, a bifurcation diagram, and Lyapunov exponents, to investigate some basic dynamical behaviours of the proposed four-dimensional system.

Abstract: A new four-dimensional quadratic smooth autonomous chaotic system is presented in this paper, which can exhibit periodic orbit and chaos under the conditions on the system parameters. Importantly, the system can generate one-, two-, three- and four-scroll chaotic attractors with appropriate choices of parameters. Interestingly, all the attractors are generated only by changing a single parameter. The dynamic analysis approach in the paper involves time series, phase portraits, Poincaré maps, a bifurcation diagram, and Lyapunov exponents, to investigate some basic dynamical behaviours of the proposed four-dimensional system.

Key words: new smooth autonomous four-dimensional chaotic system, multi-scroll chaotic attractor, Poincaré mapping, bifurcation, Lyapunov exponent

中图分类号: (Low-dimensional chaos)

05.45.Ac

05.45.Tp (Time series analysis) 02.30.Uu (Integral transforms) 02.30.Yy (Control theory)

SaraDadras, HamidRezaMomeni. Generating one-, two-, three- and four-scroll attractors from a novel four-dimensional smooth autonomous chaotic system[J]. 中国物理B, 2010, 19(6): 60506-060506.

Sara Dadras and Hamid Reza Momeni. Generating one-, two-, three- and four-scroll attractors from a novel four-dimensional smooth autonomous chaotic system[J]. Chin. Phys. B, 2010, 19(6): 60506-060506.

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Generating one-, two-, three- and four-scroll attractors from a novel four-dimensional smooth autonomous chaotic system

Generating one-, two-, three- and four-scroll attractors from a novel four-dimensional smooth autonomous chaotic system

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