Generating grid chaotic attractors via switching function based on a third-order linear system

This paper proposes a novel system for generating 1-D m-scroll, 2-D m×n-grid multi-scroll, 3-D m×n×l-grid multi-scroll chaotic attractors (GMSCAs) via switching piecewise linear (PWL) function. First, a third-order linear system satisfying certain conditions is introduced as the original system. Then, by adding stair function, saturated function series and hysteresis function series to the third-order linear system, respectively, GMSCAs are generated along a certain line, or plane, or in the whole state space. Besides, some basic dynamical behaviors of the controlled system are investigated and numerical simulations are given to verify the effectiveness of this method.