Open AccessAnalysis of the fast-slow hyperchaotic Lorenz system
Author(s) -
Xiujing Han,
Bo Jiang,
Qinsheng Bi
Publication year - 2009
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.58.6006
Subject(s) - bifurcation , bursting , coupling strength , lorenz system , chaotic , stability (learning theory) , physics , coupling (piping) , statistical physics , hopf bifurcation , control theory (sociology) , mechanics , mathematics , computer science , nonlinear system , materials science , condensed matter physics , quantum mechanics , neuroscience , control (management) , artificial intelligence , machine learning , metallurgy , biology
The stability of the origin of the hyperchaotic Lorenz system with two time scales is investigated. The characteristics of Hopf bifurcation from the origin, including the existence condition, the direction as well as the stability of bifurcating periodic solutions are discussed in detail, which can be demonstrated by the numerical simulations. With certain parameter, the fast-slow system can exhibit symmetric bursting and further lead to hyperchaotic movement. Based on the method of slow-fast analysis, different bifurcation forms between quiescent state and spiking has been revealed and the influence of coupling strength on slow passage effect is disscussed.