title: Design and implementation of grid multi-scroll fractional-order chaotic attractors.
abstract: This paper proposes a novel approach for generating multi-scroll chaotic attractors in multi-directions for fractional-order (FO) systems. The stair nonlinear function series and the saturated nonlinear function are combined to extend equilibrium points with index 2 in a new FO linear system. With the help of stability theory of FO systems, stability of its equilibrium points is analyzed, and the chaotic behaviors are validated through phase portraits, Lyapunov exponents, and Poincaré section. Choosing the order 0.96 as an example, a circuit for generating 2-D grid multiscroll chaotic attractors is designed, and 2-D 9 × 9 grid FO attractors are observed at most. Numerical simulations and circuit experimental results show that the method is feasible and the designed circuit is correct.
authors: School of Electrical Engineering and Automation, Hefei University of Technology, Hefei 230009, China.
authors: Liping
authors: L
authors: Chen
authors: School of Electrical Engineering and Automation, Hefei University of Technology, Hefei 230009, China.
authors: Wei
authors: W
authors: Pan
authors: School of Mathematics, Anhui University, Hefei 230039, China.
authors: Ranchao
authors: R
authors: Wu
authors: Department of Electrical Engineering, Institute of Engineering, Polytechnic of Porto, R. Dr. António Bernardino de Almeida, 431, 4249-015 Porto, Portugal.
authors: J A
authors: JA
authors: Tenreiro Machado
authors: UISPA-LAETA/INEGI, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal.
authors: António M
authors: AM
authors: Lopes