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  

THE INFLUENCE OF WEAK PARAMETRIC PERIODIC PERTURBATION ON SAFE BASIN AND THE CONTROL OF THE FRACTAL EROSION BASIN

作　　者：龚璞林[1] 徐健学[1] 孙政策[1] 

机构地区：[1]西安交通大学非线性动力学研究所,西安710049

出　　处：《物理学报》2001年第5期841-846,共6页Acta Physica Sinica

基　　金：国家自然科学基金(批准号 :19972 0 5 1;3 9970 2 42 )&&

摘　　要：讨论了弱参数周期扰动对于非线性系统安全域的影响 ,在一定频率下的参数周期扰动将加速安全域的分形侵蚀 ,而在另一些频率的扰动下 ,将抑制安全域的分形侵蚀 ,并且存在着增进安全域的最优频率 .提出了用弱参数周期扰动控制受到分形侵蚀的安全域的方法 ,并用Melnikov方法进行了分析 .最后讨论了这种控制安全域的方法在实际环境中当具有外加噪声时的鲁棒性 .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.

关 键 词：分形吸引域边界 参数周期扰动 控制 非线性系统 安全域 分形侵蚀 非线性振子 工程动力学 MELNIKOV方法 吸引子 

分 类 号：O316[理学—一般力学与力学基础]