Generating multi-directional multi-scroll chaotic attractors via a fractional differential hysteresis system

This Letter initiates a hysteresis series switching approach for generating multi-directional multi-scroll chaotic attractors from a three-dimensional linear autonomous fractional differential system, including 1-D n  -scroll, 2-D (n×m)(n×m)-grid scroll, and 3-D (n×m×l)(n×m×l)-grid scroll chaotic attractors. The underlying dynamical mechanisms of a fractional differential hysteresis system are then further investigated.