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...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.展开更多
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...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.展开更多
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 4...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.展开更多
The main purpose of the paper is to display the relaxation oscillations, known as the bursting phenomena, for the coupled oscillators with periodic excitation with an order gap between the exciting frequency and the n...The main purpose of the paper is to display the relaxation oscillations, known as the bursting phenomena, for the coupled oscillators with periodic excitation with an order gap between the exciting frequency and the natural frequency. For the case when the exciting frequency is much smaller than the natural frequency, different types of bursting oscillations such as fold/fold, Hopf/Hopf bursting oscillations can be observed. By regarding the whole exciting term as a slow-varying parameter on the fact that the exciting term changes on a much smaller time scale, bifurcations sets of the generalized autonomous system is derived, which divide the parameter space into several regions associated with different types of dynamical behaviors. Two cases with typical bifurcation patterns are focused on as examples to explore the dynamical evolution with the variation of the amplitude of the external excitation. Bursting oscillations which alternate between quiescent states (QSs) and repetitive spiking states (SPs) can be obtained, the mechanism of which is presented by introducing the transformed phase portraits overlapping with the bifurcation diagrams of the generalized autonomous system. It is found that not only the forms of QSs and SPs, but also the bifurcations at the transition points between QSs and SPs, may influence the structures of bursting attractors. Furthermore, the amplitudes and the frequencies related to SPs may depend on the bifurcation patterns from the quiescent sates.展开更多
A fractional-order memristor load Buck-Boost converter causes periodic system oscillation,electromagnetic noise,and other phenomena due to the frequent switching of the switch in actual operation,which is detrimental ...A fractional-order memristor load Buck-Boost converter causes periodic system oscillation,electromagnetic noise,and other phenomena due to the frequent switching of the switch in actual operation,which is detrimental to the stable operation of the power electronic converter.It is of great significance to the study of the modeling method and chaos control strategy to suppress the nonlinear behavior of the Buck-Boost converter and expand the safe and stable operation range of the power system.An estimation-correction modeling method based on a fractional active voltage-controlled memristor load peak current Buck-Boost converter is proposed.The discrete numerical solution of the state variables in the continuous mode of the inductor current is derived.The bursting oscillation phenomenon when the system introduces external excitation is analyzed.Using bifurcation,Lyapunov exponent,and phase diagrams,a large number of numerical simulations are performed.The results show that the Buck-Boost converter is chaotic for certain selected parameters,which is the prerequisite for the introduction of the controller.Based on the idea of parameter perturbation and state association,a three-dimensional hybrid control strategy for a fractional memristor Buck-Boost converter is designed.The effectiveness of the control strategy is verified by simulations,and it is confirmed that the system is controlled in a stable periodic state when the external tunable parameter s,which represents the coupling strength between the state variables in the system,gradually decreases in[-0.4,0].Compared with integer-order controlled systems,the stable operating range of fractional-order controlled systems is much larger.展开更多
基金Project supported by the Scientific Research Foundation of the National Natural Science Foundation of China–Outstanding Youth Foundation(Grant No.51622906)the National Natural Science Foundation of China(Grant No.51479173)+3 种基金the Fundamental Research Funds for the Central Universities,China(Grant No.201304030577)the Scientific Research Funds of Northwest A&F University,China(Grant No.2013BSJJ095)the Science Fund for Excellent Young Scholars from Northwest A&F University(Grant No.Z109021515)the Shaanxi Provincial Nova Program,China(Grant No.2016KJXX-55)
文摘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.
基金Project supported by the National Natural Science Foundation of China(Grant No.21276115)
文摘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.
基金Supported by the National Natural Science Foundation of China.
文摘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.
基金supported by the National Natural Science Foundation of China (Grant Nos. 11272135, 21276115, 11472115 & 11472116)the Scientific Research Innovation Foundation of Jiangsu Province (Grant No.1291480004)
文摘The main purpose of the paper is to display the relaxation oscillations, known as the bursting phenomena, for the coupled oscillators with periodic excitation with an order gap between the exciting frequency and the natural frequency. For the case when the exciting frequency is much smaller than the natural frequency, different types of bursting oscillations such as fold/fold, Hopf/Hopf bursting oscillations can be observed. By regarding the whole exciting term as a slow-varying parameter on the fact that the exciting term changes on a much smaller time scale, bifurcations sets of the generalized autonomous system is derived, which divide the parameter space into several regions associated with different types of dynamical behaviors. Two cases with typical bifurcation patterns are focused on as examples to explore the dynamical evolution with the variation of the amplitude of the external excitation. Bursting oscillations which alternate between quiescent states (QSs) and repetitive spiking states (SPs) can be obtained, the mechanism of which is presented by introducing the transformed phase portraits overlapping with the bifurcation diagrams of the generalized autonomous system. It is found that not only the forms of QSs and SPs, but also the bifurcations at the transition points between QSs and SPs, may influence the structures of bursting attractors. Furthermore, the amplitudes and the frequencies related to SPs may depend on the bifurcation patterns from the quiescent sates.
基金supported by the Natural Science Foundation of Xinjiang Uygur Autonomous Region(Nos.2022D01C367 and 2022D01E33)National Natural Science Foundation of China(Nos.52065064 and 52267010).
文摘A fractional-order memristor load Buck-Boost converter causes periodic system oscillation,electromagnetic noise,and other phenomena due to the frequent switching of the switch in actual operation,which is detrimental to the stable operation of the power electronic converter.It is of great significance to the study of the modeling method and chaos control strategy to suppress the nonlinear behavior of the Buck-Boost converter and expand the safe and stable operation range of the power system.An estimation-correction modeling method based on a fractional active voltage-controlled memristor load peak current Buck-Boost converter is proposed.The discrete numerical solution of the state variables in the continuous mode of the inductor current is derived.The bursting oscillation phenomenon when the system introduces external excitation is analyzed.Using bifurcation,Lyapunov exponent,and phase diagrams,a large number of numerical simulations are performed.The results show that the Buck-Boost converter is chaotic for certain selected parameters,which is the prerequisite for the introduction of the controller.Based on the idea of parameter perturbation and state association,a three-dimensional hybrid control strategy for a fractional memristor Buck-Boost converter is designed.The effectiveness of the control strategy is verified by simulations,and it is confirmed that the system is controlled in a stable periodic state when the external tunable parameter s,which represents the coupling strength between the state variables in the system,gradually decreases in[-0.4,0].Compared with integer-order controlled systems,the stable operating range of fractional-order controlled systems is much larger.
