Open AccessNon-smooth bifurcation analysis of a piecewise linear chaotic circuit
Author(s) -
Ji Ying,
Qinsheng Bi
Publication year - 2010
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.59.7612
Subject(s) - saddle node bifurcation , bifurcation , transcritical bifurcation , bifurcation diagram , jacobian matrix and determinant , hopf bifurcation , period doubling bifurcation , bogdanov–takens bifurcation , homoclinic bifurcation , mathematical analysis , biological applications of bifurcation theory , bifurcation theory , attractor , mathematics , infinite period bifurcation , nonlinear system , physics , quantum mechanics
The dynamics of a nonlinear capacitor circuit is investigated in this paper. The symmetric periodic solution and the chaotic attractor can be observed in numerical simulations. Furthermore, the generalized Jacobian matrix at the non-smooth boundaries is introduced to explore the non-smooth bifurcation mechanism for the periodic solutions. Discontinuous bifurcation in the combination of the Hopf bifurcation and the turning point bifurcation occurs at the non-smooth boundaries. Here, the Hopf bifurcation may result in a new frequency, which leads to periodic oscillation. With the variation of the parameter, the periodic symmetric solution oscillates more quickly, which can also be explained through non-smooth bifurcation, and the conclusion accord well with the numerical results.