Papers by Keyword: Bifurcation

Abstract: This paper derives bifurcation and chaos phenomena for the Boost converter under current-mode control. The precise discrete iterative mode is compiled in M file of MATLAB to obtain the bifurcation diagram, the Poincare mapping, the discrete value of output voltage and inductor current; The piecewise smooth switch model is built in Simulink of MATLAB to obtain the phase diagram and the time-domain chart. On the basis of two models, the bifurcation phenomena under variation of a range of circuit parameters including load resistance, have been investigated. Two kinds of model simulation results had the better consistency, which were proved the existence of bifurcation and chaos phenomena in the current-mode Boost converter.

Abstract: Bifurcation which may lead to chaos is the typical character of nonlinear system, and an asymmetric system with asymmetric parameter is adopted in this paper. The basic characteristics which vary with the asymmetric parameter are investigated firstly, and then, the second-order averaging method is used to investigate the local bifurcation of the asymmetric system. The super and sub critical saddle-node bifurcation curves of both left center and right center of the system are solved analytically. The results show that the degree of asymmetric is influenced by the value of asymmetric parameter and the two bifurcation curves of the same center are intersected at the point which also depends on the asymmetric parameter value.

Abstract: A fractional-order hyperchaotic system was proposed and some basic dynamical properties were investigated to show chaotic behavior. These properties include instability of equilibria, sensitivity to initial conditions, strange attractor, Lyapunov exponents, and bifurcation. The fractional-order system presents hyperchaos, chaos, and periodic behavior when the parameters vary continuously. Then, an analog circuit is designed on Multisim 11 and the Multisim results are agreed with the simulation results.

Abstract: A vibro-impact dynamic model of a typical single-stage spur gear train has been proposed in this study. The lumped parameter dynamic model includes the constant meshing stiffnesses, the linear time-invariant viscous damping values and the gear clearance (backlash) non-linearity allowing teeth separations. With taking account of the effect on impact of gear tooth when meshing, the dynamic equations of motion are solved for the steady period response by use of analytical method under given periodic motion conditions. The feasibility of the given periodic motion conditions is demonstrated by comparing the analytical results with that of numeric simulation method. A Poincaré map of the system is established. The stability and bifurcation of the system are studied using analytical methods. Finally, the theoretical analyses are verified using numerical simulation.

Abstract: This paper deals with two frequency parametric excitation in presence of internal resonance. The cubic nonlinearity is inserted into the equation of motion by considering the mid-line stretching of the beam. The perturbation method of multiple scales is applied directly to the governing nonlinear fourth order integro-partial differential equation of motion. This leads to a set of first order differential equations known as the reduced equations or normalized reduced equations, which are utilized to determine the additional instability zones, appeared in the trivial state stability plot, the bifurcation and stability of fixed-points, periodic, quasi-periodic, mixed mode and chaotic responses. The transition of system behaviour from stable periodic to unstable chaotic occurs through intermittency route

Abstract: The paper is focused on analysis of dynamic properties of drive systems. It describes the possible ways of stability analysis and possible ways of analysis of bifurcation of steady states and possible occurrence of chaotic behavior.

Abstract: Nonlinear bearing forces of ball bearing under five-dimensional loads are given, and five-DOF dynamic equations of rotor ball bearing system are constructed. Bifurcation of periodic motion of rotor ball bearing system in unbalance-rotating speed and radial clearance-rotating speed parametric domains are studied by use of continuation-shooting algorithm. Results show that the way of bifurcation and stability of period-1 motion vary with radial clearance and unbalance.

Abstract: For two-dimensional XYX quantum model, iPEPS algorithm can select randomly initial state evolution, and get two degenerate symmetric broken ground state wave functions. In the quantum model, not only bifurcation behavior of ground state fidelity can be used, but bifurcation behavior of reduced density matrix fidelity can also be used to determine the phase transition point and its type caused by spontaneous broken symmetry of quantum of the system. Therefore, spontaneous symmetry breaking based on fidelity bifurcation can determine quantum phase transition one quantum system had gone through. This nature provides a method to further study quantum critical phenomena in quantum multibody system

Abstract: This paper proposes a corrected shooting method for a general non-linear system with impacts. We define the global Poincaré mapping for period orbits by the discontinuous mapping. It is suitable to construct the strategy of shooting method. As an illustrated example, we investigate the stability of period orbits in a Duffing system with impacts. In Addition, coexistence of attractors and bifurcations for period orbits are considered.

Abstract: Inhibitory chemical coupling connections are ubiquitous in neuronal system. In this paper, we first reduce the complex neuronal dynamics to a simple phase model by means of phase-model reduction method. Then we examine the roles of time delays extensively on the synchronization properties by bifurcation analysis and numerical simulation. Finally, we identify the existence and the stability of various phase-locked states. Along with the expected phase and anti-phase synchronization regimes, we find the emergent phenomena that significantly influence the synchronization behavior.