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Bifurcations of a New Fractional-Order System with a One-Scroll Chaotic Attractor

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  • Xiaojun Liu
  • Ling Hong
  • Lixin Yang
  • Dafeng Tang

Abstract

In this paper, a new fractional-order system which has a chaotic attractor of the one-scroll structure is presented. Firstly, the stability of the equilibrium points of the system is investigated. And based on the stability analysis, the generation conditions of the one-scroll structure for the attractor are determined. In a commensurate-order case, bifurcations with the variation of a system parameter are investigated as derivative orders decrease from 0.99. In an incommensurate-order case, bifurcations with the variation of a derivative order are analyzed as other orders decrease from 1.

Suggested Citation

  • Xiaojun Liu & Ling Hong & Lixin Yang & Dafeng Tang, 2019. "Bifurcations of a New Fractional-Order System with a One-Scroll Chaotic Attractor," Discrete Dynamics in Nature and Society, Hindawi, vol. 2019, pages 1-15, January.
    • Handle: RePEc:hin:jnddns:8341514
    DOI: 10.1155/2019/8341514
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    Cited by:

    1. Mohammadi, Shaban & Hejazi, S. Reza, 2023. "Using particle swarm optimization and genetic algorithms for optimal control of non-linear fractional-order chaotic system of cancer cells," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 206(C), pages 538-560.

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