Generation of a family of fractional order hyper-chaotic multi-scroll attractors

Liping Chen, Wei Pan, Kunpeng Wang, Ranchao Wu, J. A. Tenreiro Machado and António M. Lopes

Chaos, Solitons & Fractals, 2017, vol. 105, issue C, 244-255

Abstract: An unified method to yield a family of fractional-order (FO) hyper-chaotic multi-scroll (HCMS) systems in Rn is proposed. Firstly, a new simple 3-dimensional (3-D) FO unstable linear system is introduced. Afterwards, additional variables are added and one nonlinear controller with adjustable parameters is included to generate HCMS attractors. A guideline to construct HCMS systems of any dimension is presented, that is verified along within the dynamics of three examples, namely 4-D, 5-D and 10-D FO HCMS systems. Phase portraits, Poincaré maps and two positive Lyapunov exponents are calculated. Moreover, a circuit of 0.96-order is also designed to realize one 4-D FO HCMS system. Numerical simulations and circuit simulation results show the feasibility of the novel approach.

Keywords: Fractional-order; Hyper-chaotic; Multi-scroll; Circuit simulation (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:105:y:2017:i:c:p:244-255

DOI: 10.1016/j.chaos.2017.10.032

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