Analysis and control of multiple chaotic attractors from a three-dimensional system

This paper studies a three-dimensional multiple chaotic system with three quadratic nonlinear terms. The system is shown to exhibit multiple periodic attractors and multiple chaotic attractors including a four-scroll chaotic attractor. It is shown analytically and numerically that any neighborhood of the four-scroll chaotic attractor contains repelling sets with positive Lebesgue measures. Moreover, in terms of incommensurate fractional order systems, a simple fractional differentiator-based controller is designed to suppress chaos. Some basic dynamical behaviors of the system are investigated through analytical techniques and numerical simulation.