物理学报2012，Vol.61Issue(18)：82-88,7.
受迫Holmes．Duffing系统安全域分形及时滞速度反馈控制
Fractal eroded safe basins in a forced Holmes-Duffing system and its control by delayed velocity feedback
摘要
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.关键词
安全域侵蚀/分形/Melnikov函数/时滞反馈控制Key words
erosion of safe basin/fractal/Melnikov function/delayed feedback control分类
数理科学引用本文复制引用
尚慧琳..受迫Holmes．Duffing系统安全域分形及时滞速度反馈控制[J].物理学报,2012,61(18):82-88,7.基金项目
国家自然科学基金（批准号：10902071）、上海市教委晨光计划（批准号：11CG61）、上海应用技术学院科学技术发展基金（批准号：KJ2011-06）和上海市教育委员会重点学科建设项目（批准号：J51501）资助的课题. （）
