An unusual chaotic system and its control

This paper reports the finding of a new chaotic system in a simple three-dimensional (3D) autonomous system with two nonlinear terms, which has rich and complex dynamical behaviors, and its control. Of particular interest is the fact that new chaotic system has a chaotic attractor, one stable node-focus and one unstable saddle-focus. To understand the complex dynamics of the system, some basic dynamical properties, such as equilibria, stability, the complete mathematical characterizations for Hopf bifurcation are rigorously derived and studied. Furthermore, the existence of singularly degenerate heteroclinic cycles for a suitable choice of parameters is investigated. Finally, the control problem of a new unusual chaotic system is investigated using negative feedback control. The ordinary feedback control, dislocated feedback control, enhancing feedback control and speed feedback control are used to suppress chaos to unstable equilibrium. The design is also illustrated with both simulations and experiments.