Keywords: 
• 安全域侵蚀 /
• 分形 /
• Melnikov函数 /
• 时滞反馈控制

Abstract: A forced Holmes-Dulling system is considered in this paper. A delayed velocity feedback is opplied to the system. The erosion of safe basin, caused by the periodic excitation, and the effects of delayed velocity feedback on the controlling of the fractal eroded safe basin are investigated. The conditions of fractal erosion of the basin boundary are obtained by the Melnikov method. Then considering the time delay as a variable parameter, the evolutions of safe basin with time delay are presented numerically by the 4th Runge-Kutta and the point-to-point mapping method. It is found that the increase of time delay can enhance the threshold of the fractal erosion of the basin boundary under a weak and positive feedback gain so as to reduce the basin erosion. These imply that the delayed velocity feedback can control the basin erosion of the system effectively.