Open AccessBifurcation control of a cubic symmetry discrete chaotic system
Author(s) -
Hui Zhang,
Yan-Dong Chu,
Ding Wangcai,
Xianfeng Li
Publication year - 2013
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.62.040202
Subject(s) - bifurcation , period doubling bifurcation , symmetry (geometry) , saddle node bifurcation , transcritical bifurcation , chaotic , bifurcation diagram , symmetry breaking , discrete symmetry , mathematics , controller (irrigation) , physics , nonlinear system , control theory (sociology) , mathematical analysis , control (management) , computer science , quantum mechanics , geometry , homogeneous space , artificial intelligence , agronomy , biology
A direct and effective linear-controller is employed to exactly control the locations of bifurcation points, both the symmetry-breaking bifurcation and the period-doubling bifurcation, in a cubic symmetry discrete system. Moreover, both the sensibility and the symmetry to the initial values of the system are analyzed. The lack of the solution branches due to the symmetry-breaking bifurcation can be reinstated temporarily by selecting the corresponding basins of attraction. The effectiveness of the controller is verified by numerical simulations.