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

Chinese Physics B 2017年第12期26卷 609-616页

作者：韩青爽陈帝伊张浩 Institute of Water Resources and Hydropower Research Northwest A & F University Yangling 712100 China Key Laboratory of Agricultural Soil and Water Engineering in Arid and Semiarid Areas Ministry of Education Northwest A & F University Yangling 712100 China

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.

关键词： bursting oscillations physical phenomena hydro-turbine governing system two time scales

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Relaxation oscillations induced by an order gap between exciting frequency and natural frequency

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Science China(Technological Sciences) 2017年第2期60卷 289-298页

作者： CHEN XiaoKe LI ShaoLong ZHANG ZhengDi BI QinSheng Faculty of Civil Engineering and Mechanics Jiangsu University Zhenjiang 212013 China Faculty of Science Jiangsu University Zhenjiang 212013 China

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.

关键词： coupled oscillators periodic excitation bursting oscillations bifurcation mechanism

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bursting mechanism in a periodic excited Duffing oscillator with nonlinear time-delay feedback

Bursting mechanism in a periodic excited Duffing oscillator ...

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第十五届全国非线性振动暨第十二届全国非线性动力学和运动稳定性学术会议

作者：余跃 Bi Qin-sheng Zhang Zheng-di Faculty of Civil Engineering and Mechanics Jiangsu University School of Science Nantong University

The paper investigates the generation of complex bursting patterns in the Duffing oscillator with nonlinear time-delayed *** patterns,including symmetric fold-fold,Hopf/Hopf and fold-Hopf bursting are obtained in the delayed equation when the periodic forcing changes *** analyze the bifurcations and dynamics of the system by regarding the delayed feedback and the periodic forcing as *** conditions of fold bifurcation as well as Hopf bifurcation and the stability related to forcing and time delay are presented,which have an intrinsic effect on the occurrence and mechanism of certain bursting *** regimes of bursting depending on the magnitude of the time delay itself and the strength of time delayed coupling are *** shows that the dynamics of the bursters in the delayed system are quite different from those of the bursters without *** particular,the time delay can be used as a tuning parameter to modulate the dynamics of bursting corresponding to the different types of the ***,the delayed bursting behaviors are illustrated by some numerical simulations.

关键词： bursting oscillations bifurcation mechanism Duffing oscillator time delay

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