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Design of a class of fractional‐order hyperchaotic multidirectional multi‐scroll attractors

In this paper, we aim to construct novel complex fractional‐order hyperchaotic multi‐scroll (FOHCMS) attractors from a simple structure by employing nonlinearities with different forming mechanism. In particular, saturated nonlinear function series, stair nonlinear function series, polynomial function, and hysteresis series are combined to extend equilibrium points in a linear stable four‐dimensional (4‐D) system to generate FOHCMS attractors. Dynamics of the designed systems are analyzed; the existence of hyperchaos is verified using two maximum positive Lyapunov exponents and Poincaré maps; multi‐scroll attractors are observed. The corresponding circuit is designed and simulated where multi‐scroll hyperchaotic attractors are observed. Numerical simulations and circuit simulation results show that our design is feasible.