Generating high-dimensional grid multi-scroll attractors via feedback controller and switching function

Abstract

This paper proposes a systematically method for generating high-dimensional grid multi-scroll attractors (GMSAs), including 3-D, 4-D, 5-D and even higher-dimensional GMSAs. Firstly, based on a third-order linear system, higher-order linear systems are constructed by introducing state feedback controllers. Then, switching piecewise linear (PWL) functions, including stair function and saturated series function, are introduced, respectively, to make the higher-order systems generate high-dimensional GMSAs. Besides, some basic dynamical properties of GMSA systems are investigated and numerical simulations are given to demonstrate the feasibility of the proposed method.