In order to use delayed feedback controlling erosion of safe basins in nonlinear systems, a softening Duffing oscillator was considered here as an example, a linear delayed velocity feedback was induced to the system, and the effects of the delayed velocity feedback on controlling basin erosion were investigated. Firstly, the condition of fractal erosion of safe basin's boundary of the delayed controlled system was obtained by using Melnikov method. Then, considering time delay as a variable parameter and employing 4th-order Runge-Kutta and Monte-Carlo methods, the evolutions of boundaries and the area of safe basins with the delay were presented. It was found that the delayed velocity feedback can greatly affect the safe basin, and the erosion of the safe basin can be reduced with increase in the time delay effectively. It was shown that the delayed velocity feedback can be used as a good approach to control erosion of safe basins.%为了利用时滞反馈对于非线性系统实施安全盆侵蚀控制,以一个软弹簧Duffing系统为例,对系统引入线性时滞速度反馈,研究时滞速度反馈对系统安全盆侵蚀的控制作用.首先通过Melnikov函数法分析时滞受控系统的安全盆的边界分形条件;再以时间滞后量为变参数,通过四阶龙格-库塔法和蒙特-卡罗方法,刻画安全盆形态,计算安全盆面积.发现时滞速度反馈对影响安全盆边界有着重要作用,通过增大时滞量,可以对系统的安全盆侵蚀进行有效抑制.该研究结果说明时滞速度反馈是控制系统的安全盆侵蚀的有效手段.
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