Generating one-, two-, three- and four-scroll attractors from a novel four-dimensional smooth autonomous chaotic system |
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Authors: | Sara Dadras and Hamid Reza Momeni |
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Institution: | Automation and Instruments Lab, Electrical Engineering Department, Tarbiat Modares University, P.O. Box 14115-143, Tehran, Iran |
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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, Poincar\'{e} maps,
a bifurcation diagram, and Lyapunov exponents, to investigate some
basic dynamical behaviours of the proposed four-dimensional system. |
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Keywords: | new smooth autonomous four-dimensional chaotic system multi-scroll chaotic attractor Poincar\'{e} mapping bifurcation Lyapunov exponent |
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