Generating 3-D multi-scroll chaotic attractors: A hysteresis series switching method

This paper introduces a systematic method—a hysteresis series switching approach—for generating multi-scroll chaotic attractors from a three-dimensional linear autonomous system, including 1-D n-scroll, 2-D n×m-grid scroll, and 3-D n×m×l-grid scroll chaotic attractors. The chaos generation mechanism is studied by analyzing the system trajectories and the hysteresis switching dynamics of the controlled chaotic systems are explored. Moreover, a two-dimensional Poincaré return map is rigorously derived. This map and its maximum Lyapunov exponent are applied to verifying the chaotic behaviors of the generated 3-D multi-scroll chaotic attractors.