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

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.