Generating two simultaneously chaotic attractors with a switching piecewise-linear controller

It has been demonstrated that a piecewise-linear system can generate chaos under suitable conditions. This paper proposes a novel method for simultaneously creating two symmetrical chaotic attractor––an upper-attractor and a lower-attractor––in a 3D linear autonomous system. Basically dynamical behaviors of this new chaotic system are further investigated. Especially, the chaos formation mechanism is explored by analyzing the structure of fixed points and the system trajectories.