Open AccessNon-smooth bifurcation in nonlinear electrical circuits with multiple switching boundaries
Author(s) -
Zheng Yin,
Qinsheng Bi
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.60.070507
Subject(s) - bifurcation , jacobian matrix and determinant , bursting , nonlinear system , bifurcation diagram , control theory (sociology) , boundary (topology) , saddle node bifurcation , physics , biological applications of bifurcation theory , transcritical bifurcation , mathematical analysis , period doubling bifurcation , mathematics , computer science , quantum mechanics , control (management) , neuroscience , artificial intelligence , biology
The fast-slow dynamics of a nonlinear electrical circuit with multiple switching boundaries is investigated in this paper. For suitable parameters, periodic bursting phenomenon can be observed. The full system can be divided into slow and fast subsystems because of the difference between variational speeds of state variables. According to the slow-fast analysis, the slow variable, which modulates the behavior of the system, can be treated as a quasi-static bifurcation parameter for the fast subsystem to analyze the stabilities of equilibrium points in different areas of vector field. The bifurcation is dependent on the switching boundary in the vector field. In particular, for the two-time scale non-smooth system with fast-slow effect, the bifurcation of fast subsystem is determined by the characteristics of equilibrium points on both sides of the switching boundary. Furthermore, the generalized Jacobian matrix at the non-smooth boundary is introduced to explore the type of non-smooth bifurcation (i.e., multiple crossing bifurcation) in the fast subsystem, which can also be used to explain the mechanism for symmetric bursting phenomenon of the full system.