The method of moments is applied to an underdamped bistable oscillator driven by Gaussian white noise and a weak periodic force for the observations of stochastic resonance and the resulting resonant structures are compared with those from Langevin simulation. The physical mechanisms of the stochastic resonance are explained based on the evolution of the intrawell frequency peak and the above-barrier frequency peak via the noise intensity and the fluctuation-dissipation theorem, and the three possible sources of stochastic resonance in the system are confirmed. Additionally, with the noise intensity fixed, the stochastic resonant structures are also observed by adjusting the nonlinear parameter.

In this paper, the dynamic stability of a shallowarch with elastic supports subjected to impulsive load is used as a theoretical model to investigate the dynamic stability problem of inner windings of power transformer under short-circuit condition. Firstly, the series solution representing the equilibrium conogurations of a shallowarch is obtained by solving the corresponding non-linear integration-di1erential equation. The local stability of each equilibrium conoguration is discussed, and the su-cient condition for stability of the shallowarch system as well as the critical load against snap-through is obtained. Secondly, the equivalent relation between short-circuit load and impulsive one, and the electrical forces transferred pattern between the coils of inner windings are assumed. Then the results of the shallowarch model are applied to the case of the inner winding of transformer and the formulas for computing critical electromagnetic force and the dynamic stability criterion of the inner windings are established. Finally, examples are o1ered and the theoretical results are shown to agree well with the experimental ones.

We have analyzed the responses of an excitable FitzHugh-Nagumo neuron model to a weak periodic signal with and without noise. In contrast to previous studies which have dealt with stochastic resonance in the excitable model when the model with periodic input has only one stable attractor, we have focused our attention on the relationship between the global dynamics of the forced excitable neuron model and stochastic resonance. Our results show that for some parameters the forced FitzHugh-Nagumo neuron model has two attractors: the small-amplitude subthreshold periodic oscillation and the large-amplitude suprathreshold periodic oscillation. Random transitions between these two periodic oscillations are the essential mechanism underlying stochastic resonance in this model. Differences of such stochastic resonance to that in a classical bistable system and the excitable system are discussed. We also report that the state of the basin of attraction has a significant effect on the stability of neuronal firings, in the sense that the fractal basin boundary of the system enhances the noise-induced transitions.

In this Letter, a generalized cell mapping digraph method is presented on the basis of a correspondence between the generalized cell mapping of dynamical systems and digraphs, and this correspondence is theoretically proved on the basis of set theory in the cell state space. State cells are classified afresh, and self-cycling sets, persistent self-cycling sets and transient self-cycling sets are defined. The algorithms of digraphs are adopted for the purpose of determining the global evolution properties of the systems. After all the self-cycling sets are condensed by using the digraphic condensation method, a topological sorting of the global transient state cells can be efficiently achieved. Based on the different treatments, the global properties can be divided into qualitative and quantitative properties. In the analysis of the qualitative properties, only Boolean operations are used. As a result, the complicated behavior of nonlinear dynamical systems can be efficiently studied in a new way. A boundary crisis is studied by means of the generalized cell mapping digraph method. Attractors, basins, basin boundaries and unstable solutions are obtained once through a global analysis at low computational cost. Moreover, the approach of a chaotic attractor to an unstable periodic orbit at its basin boundary before a boundary crisis, the collision of the chaotic attractor with the unstable periodic orbit when the crisis occurs, and a chaotic transient after the crisis, are explicitly shown. The limiting probability distribution of the chaotic attractor is calculated.

ln this paper, a continuous fourth-order ordinary differential equation Shanley-type model is suggested for analytical analysis of the problem of elastic-plastic beam dynamics. A co-dimension three bifurcation problem and its simplified case, an incomplete co-dimension two bifurcation of a pair of pure imaginary eigenvalues and a simple zero eigenvalue are presented and analyzed, and the normal form analysis and the unfoldings of 2-jet and 4-jet cases of the incomplete normal forms are provided. Since elastic-Plastic beam dynamics are of great non-linear complexity and the vector fields are multiple degeneracies, small differences of physical parameters cause dramatic essential changes of behavior of the motion. Through these results the rich dynamical behaviors of the elastic plastic beam dynamics, including the counterintuitive behavior and its sensitivity to small parameters of this problem, can be illustrated. Copyright.