In this paper we report a kind of fast-scale instability occurring in the single-ended primary inductance converter （SEPIC） power factor pre-regulator, which is designed to operate in discontinuous conduction mode. ...In this paper we report a kind of fast-scale instability occurring in the single-ended primary inductance converter （SEPIC） power factor pre-regulator, which is designed to operate in discontinuous conduction mode. Main results are given by exact cycle-by-cycle computer simulations as well as theoretical analysis. It is found that the instability phenomenon manifests itself as a fast-scale bifurcation at the switching period, which implies the occurrence of border collision bifurcation, or is related to the transition of the regular operating mode of the SEPIC. According to the theoretical analysis and simulation results, the effects of parameters on system stability, and the locations of the bifurcation points are confirmed. Moreover, the effects of such an instability on power factor and switching stress are also discussed. Finally, the occurrence of the asymmetric bifurcation locations is investigated. The results show that this work provides a convenient means of predicting stability boundaries which can facilitate the selection of the practical parameters.展开更多
A variety of border collision bifurcations in a three-dimensional （3D） piecewise smooth chaotic electrical circuit are investigated. The existence and stability of the equilibrium points are analyzed. It is found th...A variety of border collision bifurcations in a three-dimensional （3D） piecewise smooth chaotic electrical circuit are investigated. The existence and stability of the equilibrium points are analyzed. It is found that there are two kinds of non-smooth fold bifurcations. The existence of periodic orbits is also proved to show the occurrence of non-smooth Hopf bifurcations. As a composite of non-smooth fold and Hopf bifurcations, the multiple crossing bifurcation is studied by the generalized Jacobian matrix. Some interesting phenomena which cannot occur in smooth bifurcations are also considered.展开更多
Based on the bifurcation theory in nonlinear dynamics, this paper analyzes quantitatively period solution dynamic characteristic. In particular, the ones of period-1 and period-2 solutions are deeply studied. From loc...Based on the bifurcation theory in nonlinear dynamics, this paper analyzes quantitatively period solution dynamic characteristic. In particular, the ones of period-1 and period-2 solutions are deeply studied. From locus of Jacobian matrix eigenvalue, we conclude that the bifurcations between period-1 and period-2 solutions are pitchfork bifurcations while the bifurcations between period-2 and period-3 solutions are border collision bifurcations. The double period bifurcation condition is verified from complex plane locus of eigenvalues, furthermore, the necessary condition occurred pitchfork bifurcation is obtained from the cause of border collision bifurcation.展开更多
A new simple piecewise linear map of the plane is presented and analyzed, then a detailed study of its dynamical behaviour is described, along with some other dynamical phenomena, especially fixed points and their sta...A new simple piecewise linear map of the plane is presented and analyzed, then a detailed study of its dynamical behaviour is described, along with some other dynamical phenomena, especially fixed points and their stability, observation of a new chaotic attractors obtained via border collision bifurcation. An important resuk about coexisting chaotic attractors is also numerically studied and discussed.展开更多
文摘In this paper we report a kind of fast-scale instability occurring in the single-ended primary inductance converter （SEPIC） power factor pre-regulator, which is designed to operate in discontinuous conduction mode. Main results are given by exact cycle-by-cycle computer simulations as well as theoretical analysis. It is found that the instability phenomenon manifests itself as a fast-scale bifurcation at the switching period, which implies the occurrence of border collision bifurcation, or is related to the transition of the regular operating mode of the SEPIC. According to the theoretical analysis and simulation results, the effects of parameters on system stability, and the locations of the bifurcation points are confirmed. Moreover, the effects of such an instability on power factor and switching stress are also discussed. Finally, the occurrence of the asymmetric bifurcation locations is investigated. The results show that this work provides a convenient means of predicting stability boundaries which can facilitate the selection of the practical parameters.
基金Project supported by the National Natural Science Foundation of China(Nos.11272024,11371046,and 11372017)the Fundamental Research Funds for the Central Universities
文摘A variety of border collision bifurcations in a three-dimensional （3D） piecewise smooth chaotic electrical circuit are investigated. The existence and stability of the equilibrium points are analyzed. It is found that there are two kinds of non-smooth fold bifurcations. The existence of periodic orbits is also proved to show the occurrence of non-smooth Hopf bifurcations. As a composite of non-smooth fold and Hopf bifurcations, the multiple crossing bifurcation is studied by the generalized Jacobian matrix. Some interesting phenomena which cannot occur in smooth bifurcations are also considered.
基金This work was supported by the National Nature Science Foundation of China under Grant No.60436030
文摘Based on the bifurcation theory in nonlinear dynamics, this paper analyzes quantitatively period solution dynamic characteristic. In particular, the ones of period-1 and period-2 solutions are deeply studied. From locus of Jacobian matrix eigenvalue, we conclude that the bifurcations between period-1 and period-2 solutions are pitchfork bifurcations while the bifurcations between period-2 and period-3 solutions are border collision bifurcations. The double period bifurcation condition is verified from complex plane locus of eigenvalues, furthermore, the necessary condition occurred pitchfork bifurcation is obtained from the cause of border collision bifurcation.
文摘A new simple piecewise linear map of the plane is presented and analyzed, then a detailed study of its dynamical behaviour is described, along with some other dynamical phenomena, especially fixed points and their stability, observation of a new chaotic attractors obtained via border collision bifurcation. An important resuk about coexisting chaotic attractors is also numerically studied and discussed.
