Open AccessControlling fractal erosion of safe basins in a Helmholtz oscillator by delayed position feedback
Author(s) -
Huilin Shang
Publication year - 2011
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.60.070501
Subject(s) - fractal , erosion , position (finance) , structural basin , control theory (sociology) , point (geometry) , geology , mechanics , physics , computer science , mathematics , geometry , mathematical analysis , control (management) , geomorphology , finance , artificial intelligence , economics
A linear delayed position feedback is introduced into a Helmholtz oscillator system, and its effects on controlling the erosion of safe basins are investigated. The condition of fractal erosion of the basin boundary of the delayed feedback controlled system is acquired, there by the threshold of the excitation of the fractal erosion is obtained. Then considering time delay as a variable parameter and employing the 4th-order Runge-Kutta method and the point-to-point mapping method, evolutions of safe basins with time delay are presented. It is found that the increasing of time delay can enhance the threshold of the fractal erosion and reduce the erosion of safe basin effectively under a weak feedback gain. All the results imply that delayed position feedback can be used as a good strategy to control the erosion of safe basins.