THE INFLUENCE OF WEAK PARAMETRIC PERIODIC PERTURBATION ON SAFE BASIN AND THE CONTROL OF THE FRACTAL EROSION BASIN
弱的参数周期扰动对一非线性系统安全域的影响与分形侵蚀安全域的控制

In this paper,the influence of weak parameter periodic perturbation on the safe basin of a nonlinear oscillator is studied.The results show that the fractal erosion of the safe basin is enhanced when the system is perturbed by the periodic signal at some definite frequencies.On the other hand,the fractal erosion basin is suppressed by the periodic perturbation at other frequencies,for this case there exists an optimal perturbation frequency.Furthermore,based on the obtained results,a method used to control the fractal erosion basin is presented.Melnikov's method is used to interpret this control method,and the robustness of the control of the fractal erosion basin is also discussed.