Open AccessBifurcation control for a non-autonomous system with two time delays
Author(s) -
Qian Chang-zhao,
Jinlu Tang
Publication year - 2006
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.55.617
Subject(s) - bifurcation , transcritical bifurcation , saddle node bifurcation , bifurcation diagram , homoclinic bifurcation , biological applications of bifurcation theory , bifurcation theory , control theory (sociology) , period doubling bifurcation , perturbation (astronomy) , infinite period bifurcation , bogdanov–takens bifurcation , mathematics , mathematical analysis , physics , computer science , control (management) , nonlinear system , quantum mechanics , artificial intelligence
A forced system with two time-delays, including van der Pol-Duffing types, is studied. The aim is to study the primary parametrical resonance bifurcation of this system. Perturbation method is used to obtain the bifurcation equation with time-delays. Based on the bifurcation equation, co-dimension one, co-dimension two and Hope bifurcation are discussed, and the effect of time-delays on the steady state response is analyzed by numerical methods. It is indicated that the primary resonance bifurcation can be well controlled by time-delays feedback.