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Generation of a family of fractional order hyper-chaotic multi-scroll attractors. (English) Zbl 1380.34119

Summary: 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.

MSC:

34K37 Functional-differential equations with fractional derivatives
34K23 Complex (chaotic) behavior of solutions to functional-differential equations
37M05 Simulation of dynamical systems
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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