Generation of a family of fractional order hyper-chaotic multi-scroll attractors. (December 2017)

• Record Type: Journal Article
• Authors: Chen, Liping; Pan, Wei; Wang, Kunpeng; Wu, Ranchao; Machado, J. A. Tenreiro; Lopes, António M.
• Is Part Of: Chaos, solitons and fractals. Volume 105(2017)
• Page Start: 244
• Page End: 255
• Publication Date: 2017-12
• Subjects: Fractional-order -- Hyper-chaotic -- Multi-scroll -- Circuit simulation; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2017.10.032
• Languages: English
• ISSNs: 0960-0779

Abstract

Abstract: An unified method to yield a family of fractional-order (FO) hyper-chaotic multi-scroll (HCMS) systems in R n 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.