Bursting oscillations in a hydro-turbine governing system with two time scales

A fast-slow coupled model of the hydro-turbine governing system （HTGS） is established by introducing frequency disturbance in this paper. Based on the proposed model, the performances of two time scales for bursting oscillations in the HTGS are investigated and the effect of periodic excitation of frequency disturbance is analyzed by using the bifurcation diagrams, time waveforms and phase portraits. We find that stability and operational characteristics of the HTGS change with the value of system parameter kd. Furthermore, the comparative analyses for the effect of the bursting oscillations on the system with different amplitudes of the periodic excitation a are carried out. Meanwhile, we obtain that the relative deviation of the mechanical torque mt rises with the increase of a. These methods and results of the study, combined with the performance of two time scales and the fast-slow coupled engineering model, provide some theoretical bases for investigating interesting physical phenomena of the engineering system.

Bursting phenomena as well as the bifurcation mechanism in a coupled BVP oscillator with periodic excitation

We explore the complicated bursting oscillations as well as the mechanism in a high-dimensional dynamical system.By introducing a periodically changed electrical power source in a coupled BVP oscillator, a fifth-order vector field with two scales in frequency domain is established when an order gap exists between the natural frequency and the exciting frequency.Upon the analysis of the generalized autonomous system, bifurcation sets are derived, which divide the parameter space into several regions associated with different types of dynamical behaviors. Two typical cases are focused on as examples,in which different types of bursting oscillations such as sub Hopf/sub Hopf burster, sub Hopf/fold-cycle burster, and doublefold/fold burster can be observed. By employing the transformed phase portraits, the bifurcation mechanism of the bursting oscillations is presented, which reveals that different bifurcations occurring at the transition between the quiescent states（QSs） and the repetitive spiking states（SPs） may result in different forms of bursting oscillations. Furthermore, because of the inertia of the movement, delay may exist between the locations of the bifurcation points on the trajectory and the bifurcation points obtained theoretically.

Comparison between Windowed FFT and Hilbert-Huang Transform for Analyzing Time Series with Poissonian Fluctuations: A Case Study

Hilbert-Huang Transform （HHT） is a novel data analysis technique for nonlinear and non-stationary data. We present a time-frequency analysis of both simulated fight curves and an X-ray burst from the X-ray burster 4U 1702-429 with both the HHT and the Windowed Fast Fourier Transform （WFFT） methods. Our results show that the HHT method has failed in all cases for light curves with Poissonian fluctuations which axe typical for all photon counting instruments used in astronomy, whereas the WFFT method can sensitively detect the periodic signals in the presence of Poissonian fluctuations; the only drawback of the WFFT method is that it cannot detect sharp frequency variations accurately.