Bursting phenomena as well as the bifurcation mechanism in controlled Lorenz oscillator with two time scales

Bi, Qinsheng; Zhang, Zhengdi

doi:10.1016/j.physleta.2011.01.037

Cited by 48 publications

(10 citation statements)

References 17 publications

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“…e introduction of the slow-fast dynamics analysis method [19] well explained the bifurcation connection between the spiking state and the quiescent state, so as the mechanism of bursting oscillation. Based on this method, various bursting oscillation modes [20][21][22][23][24][25][26][27][28][29][30][31][32][33] are obtained, such as fold/fold bursting and fold/ Hopf bursting. In nonlinear dynamical system, two time scales can lead to complex dynamical behavior of the system, so it is widely concerned by academic circles domestically and overseas.…”

Section: Introductionmentioning

confidence: 99%

Bursting Oscillation and Its Mechanism of a Generalized Duffing–Van der Pol System with Periodic Excitation

2021

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The complex bursting oscillation and bifurcation mechanisms in coupling systems of different scales have been a hot spot domestically and overseas. In this paper, we analyze the bursting oscillation of a generalized Duffing–Van der Pol system with periodic excitation. Regarding this periodic excitation as a slow-varying parameter, the system can possess two time scales and the equilibrium curves and bifurcation analysis of the fast subsystem with slow-varying parameters are given. Through numerical simulations, we obtain four kinds of typical bursting oscillations, namely, symmetric fold/fold bursting, symmetric fold/supHopf bursting, symmetric subHopf/fold cycle bursting, and symmetric subHopf/subHopf bursting. It is found that these four kinds of bursting oscillations are symmetric. Combining the transformed phase portrait with bifurcation analysis, we can observe bursting oscillations obviously and further reveal bifurcation mechanisms of these four kinds of bursting oscillations.

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Section: Introductionmentioning

confidence: 99%

Bursting Oscillation and Its Mechanism of a Generalized Duffing–Van der Pol System with Periodic Excitation

2021

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“…Over the past few decades, a large number of BOs with different bifurcation mechanisms have been investigated. For instance, in some two-timescale system [13][14][15][16], fold/fold, fold/Hopf and symmetric Hopf/Hopf burster have been observed. Recently, more complex BOs are found on multi-timescale systems.…”

Section: Introductionmentioning

confidence: 99%

Multi-bifurcation cascaded bursting oscillations and mechanism in a novel 3D non-autonomous circuit system with parametric and external excitation

Wang

Zhang

et al. 2021

Nonlinear Dyn

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In this paper, multi-timescale dynamics and the formation mechanism of a 3D non-autonomous system with two slowly varying periodic excitations are systematically investigated. Interestingly, the system shows novel multibifurcation cascaded bursting oscillations (MBCBOs) when the frequency of the two excitations is much lower than the mean frequency of the original system (MFOS). For instance, periodic, quasi-periodic and chaotic bursting oscillations induced by a variety of cascaded bifurcations are first observed, and the phenomenon of spiking transfer is also revealed. Besides, stability and local bifurcations of the system are comprehensively investigated to analyze the mechanism of the observed MBCBOs, in which bifurcation diagram, Lyapunov exponents, time series, phase portraits, and transformed phase diagrams are used. Finally, through a circuit simulation and hardware experiment, these complex dynamics phenomena are verified physically.

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“…The system involves multi-timescales in operation because of the different response rates of these subsystems, which leads to the occurrence of richer dynamic behaviors compared with the same scale, such as bursting oscillation. Such oscillation, known as the quiescent state (QS) and spiking state (SP), is characterized by the combination of large amplitude oscillations and small amplitude oscillations in each period, which may lead to some special forms of bursting phenomena (Izhikevich, 2000; Bi and Zhang, 2011 ; Zhang et al., 2013; Sakaguchi and Okita, 2016 ; Shin et al., 2017; Zhang et al., 2018a). This special phenomenon has great influence on the safe and stable operation of a hydropower station.…”

Section: Introductionmentioning

confidence: 99%

Fast–slow dynamic behaviors of a hydraulic generating system with multi-timescales

Zhang¹,

Chen

Zhang³

et al. 2019

Journal of Vibration and Control

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Hydraulic generating systems are widely modeled in the literature for investigating their stability properties by means of transfer functions representing the dynamic behavior of the reservoir, penstock, surge tank, hydro-turbine, and the generator. Traditionally, in these models the electrical load is assumed constant to simplify the modeling process. This assumption can hide interesting dynamic behaviors caused by fluctuation of the load as actually occurred. Hence, in this study, the electrical load characterized with periodic excitation is introduced into a hydraulic generating system and the responses of the system show a novel dynamic behavior called the fast–slow dynamic phenomenon. To reveal the nature of this phenomenon, the effects of the three parameters (i.e., differential adjustment coefficient, amplitude, and frequency) on the dynamic behaviors of the hydraulic generating system are investigated, and the corresponding change rules are presented. The results show that the intensity of the fast–slow dynamic behaviors varies with the change of each parameter, which provides reference for the quantification of the hydraulic generating system parameters. More importantly, these results not only present rich nonlinear phenomena induced by multi-timescales, but also provide some theoretical bases for maintaining the safe and stable operation of a hydropower station.

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Bursting phenomena as well as the bifurcation mechanism in controlled Lorenz oscillator with two time scales

Cited by 48 publications

References 17 publications

Bursting Oscillation and Its Mechanism of a Generalized Duffing–Van der Pol System with Periodic Excitation

Bursting Oscillation and Its Mechanism of a Generalized Duffing–Van der Pol System with Periodic Excitation

Multi-bifurcation cascaded bursting oscillations and mechanism in a novel 3D non-autonomous circuit system with parametric and external excitation

Fast–slow dynamic behaviors of a hydraulic generating system with multi-timescales

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