Chaos Control of Lauwerier Mapping

In order to overcome the defect that the properties of the original system is changed in the process of chaos control with external excitation or damping, the OGY control method is combined with the pole placement technique of the linear control theory to establish a linear mapping. By applying the pole placement technique to select a small time-dependent perturbation of the control parameter, a new method is proposed to control the chaos movement of Lauwerier mapping. According to the ergodicity of chaos movement, the unstable periodic orbits are embedded into the chaotic attractor. The unstable period-1 and period-2 orbits are selected as the control targets. When map points wander to the neighborhood of these periodic orbits, a small perturbation is added to the system control parameter, and the unstable period-1 and period-2 orbits are controlled to be stable. In addition, the influence of different regulator poles on the control time is analyzed. The results show that when the two poles are 1/8 and 0, respectively, the unstable period-1 orbit is controlled at the fixed point after 230 iterations; and when the two poles are 1/6 and -1/4, the chaos control is achieved after 3 300 iterations. The dynamic properties of the original system is not changed in the process of the chaos control.