Open AccessHybrid control of bifurcation in a predator-prey system with three delays
Author(s) -
Liping Zhang,
Min Xu,
Huinan Wang
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.60.010506
Subject(s) - saddle node bifurcation , center manifold , transcritical bifurcation , hopf bifurcation , biological applications of bifurcation theory , pitchfork bifurcation , bifurcation diagram , homoclinic bifurcation , period doubling bifurcation , bogdanov–takens bifurcation , mathematics , control theory (sociology) , bifurcation , mathematical analysis , computer science , physics , control (management) , nonlinear system , quantum mechanics , artificial intelligence
The problem of Hopf bifurcation control for a predator-prey system with three delays is considered. A new hybrid strategy is proposed to control the Hopf bifurcation, in which the state feedback and parameter perturbation are used to delay the onset of an inherent bifurcation or make the bifurcation disappear. The stability and the existence of bifurcation are researched. In particular, the formulae determining the direction of the bifurcations and the stability of the bifurcating periodic solutions are derived by using the normal form theory and center manifold theorem. Finally, numerical simulation results confirm that the new hybrid controller is efficient in controlling Hopf bifurcation.