Open AccessFractal eroded safe basins in a forced Holmes-Duffing system and its control by delayed velocity feedback
Author(s) -
Huilin Shang
Publication year - 2012
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.61.180506
Subject(s) - structural basin , fractal , erosion , boundary (topology) , control theory (sociology) , point (geometry) , geology , mechanics , physics , computer science , mathematics , mathematical analysis , geometry , control (management) , geomorphology , artificial intelligence
A forced Holmes-Duffing 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.