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Analysis of a new 3D smooth autonomous system with different wing chaotic attractors and transient chaos

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Abstract

This letter proposes a new 3D quadratic autonomous chaotic system which displays an extremely complicated dynamical behavior over a large range of parameters. The new chaotic system has five real equilibrium points. Interestingly, this system can generate one-wing, two-wing, three-wing and four-wing chaotic attractors and periodic motion with variation of only one parameter. Besides, this new system can generate two coexisting one-wing and two coexisting two-wing attractors with different initial conditions. Furthermore, the transient chaos phenomenon happens in the system. Some basic dynamical behaviors of the proposed chaotic system are studied. Furthermore, the bifurcation diagram, Lyapunov exponents and Poincaré mapping are investigated. Numerical simulations are carried out in order to demonstrate the obtained analytical results. The interesting findings clearly show that this is a special strange new chaotic system, which deserves further detailed investigation.

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Authors and Affiliations

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

    Sara Dadras & Hamid Reza Momeni

  2. F’SATIE and Department of Electrical Engineering, Tshwane University of Technology, Peritoria, 0001, South Africa

    Guoyuan Qi

Authors
  1. Sara Dadras
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  2. Hamid Reza Momeni
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  3. Guoyuan Qi
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Correspondence to Hamid Reza Momeni.

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Dadras, S., Momeni, H.R. & Qi, G. Analysis of a new 3D smooth autonomous system with different wing chaotic attractors and transient chaos. Nonlinear Dyn 62, 391–405 (2010). https://doi.org/10.1007/s11071-010-9726-2

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  • DOI: https://doi.org/10.1007/s11071-010-9726-2

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