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A fractional order chaotic system with a 3D grid of variable attractors

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  • Munoz-Pacheco, J.M.
  • Zambrano-Serrano, E.
  • Volos, Ch.
  • Tacha, O.I.
  • Stouboulos, I.N.
  • Pham, V.-T.

Abstract

A novel fractional order dynamical system with a variable double-scroll attractor on a line, lattice and 3D grid is introduced. This system belongs to a class of chaotic systems with adjustable variables but with fractional order. Chaos generation only depends on the value of fractional order. As a result, a chaotic attractor is discovered and propagated in y-line. By introducing two extra control parameters, we also observed that the chaotic attractor varies in x-line, z-line, x−y-lattice, x−z-lattice, y−z-lattice, and 3D-grid. Dynamics of the new system are discovered by using phase portraits, bifurcation diagrams, Lyapunov spectrum, Kaplan–Yorke dimension, dissipative measure. Finally, the proposed fractional order system is designed with analog electronic circuits. Circuit results are in concordance with theoretical findings.

Suggested Citation

  • Munoz-Pacheco, J.M. & Zambrano-Serrano, E. & Volos, Ch. & Tacha, O.I. & Stouboulos, I.N. & Pham, V.-T., 2018. "A fractional order chaotic system with a 3D grid of variable attractors," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 69-78.
    • Handle: RePEc:eee:chsofr:v:113:y:2018:i:c:p:69-78
    DOI: 10.1016/j.chaos.2018.05.015
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