Design and implementation of grid multi-scroll fractional-order chaotic attractors

摘要

This paper proposes a novel approach for generating multi-scroll chaotic attractors in multidirectionsfor fractional-order (FO) systems. The stair nonlinear function series and the saturatednonlinear 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 Poincarésection. Choosing the order 0.96 as an example, a circuit for generating 2-D grid multiscroll chaoticattractors is designed, and 2-D 9x9 grid FO attractors are observed at most. Numerical simulationsand circuit experimental results show that the method is feasible and the designed circuit is correct.