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Design of fractional-order hyper-chaotic multi-scroll systems based on hysteresis series

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Abstract

This paper develops a novel fractional-order (FO) hyper-chaotic multi-scroll (FOHMS) system derived from a 4-dimensional FO linear system. Hysteresis function series are employed and added to the original system to extend the number of equilibrium points with index 2. The hyper-chaotic dynamics of the new FOHMS system is explored through phase portraits, largest Lyapunov exponents and Poincaré maps. A circuit for the 0.96-order FOHMS is implemented and several FOHMS attractors are observed. Numerical and circuit-based simulations show the feasibility of the theoretical formulation.

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Authors and Affiliations

  1. School of Electrical Engineering and Automation, Hefei University of Technology, Hefei, 230009, P.R. China

    Liping Chen, Wei Pan & Yigang He

  2. Institute of Engineering, Polytechnic of Porto, Department of Electrical Engineering, R. Dr. António Bernardino de Almeida, 431, 4249-015, Porto, Portugal

    J. A. Tenreiro Machado

  3. UISPA–LAETA/INEGI, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465, Porto, Portugal

    António M. Lopes

  4. School of Mathematics, Anhui University, Hefei, 230039, P.R. China

    Ranchao Wu

Authors
  1. Liping Chen
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  2. Wei Pan
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  3. J. A. Tenreiro Machado
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  4. António M. Lopes
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  5. Ranchao Wu
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  6. Yigang He
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Correspondence to Liping Chen.

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Chen, L., Pan, W., Tenreiro Machado, J.A. et al. Design of fractional-order hyper-chaotic multi-scroll systems based on hysteresis series. Eur. Phys. J. Spec. Top. 226, 3775–3789 (2017). https://doi.org/10.1140/epjst/e2018-00012-8

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  • DOI: https://doi.org/10.1140/epjst/e2018-00012-8

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