Dynamical study of VDPCL oscillator: antimonotonicity, bursting oscillations, coexisting attractors and hardware experiments

Tegnitsap, Joakim Vianney Ngamsa; Fotsin, Hilaire Bertrand; Tamba, Victor Kamdoum; Ngouonkadi, Elie Bertrand Megam

doi:10.1140/epjp/s13360-020-00572-9

Cited by 14 publications

(10 citation statements)

References 36 publications

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“…On the other hand, for { } Î n 3, 5 the study enabled us to obtain the following eigenvalues l = 0 and ( ( ) ) l e p = k 1 . 2 This allowed us to see that A is unstable for = k 0 and stable for ¹ k 0 [52]. In addition, as in the classical case, the dynamics obtained are sinusoidal for e = 0.1 and relaxation for e = 5.0.…”

Section: Van Der Pol Model With Sinusoidal Non-linearitymentioning

confidence: 58%

“…With the evolution of research, a great deal of work is now being carried out using non-linear oscillators [1][2][3][4][5]. These oscillators are the starting points for the analysis of non-linear behaviour [6][7][8], since most physical phenomena in life in general and in science in particular are interpreted using non-linear analysis tools [8][9][10].…”

Section: Introductionmentioning

confidence: 99%

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Dynamical behavior analysis of the Van der Pol oscillator with sine nonlinearity subjected to non-sinusoidal periodic excitations by the bifurcation structures

et al. 2023

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The present work studies the dynamical behavior of the Van der Pol oscillator with sine nonlinearity oscillator subjected to the effects of non-sinusoidal excitations through the analysis of bifurcation structures. In this work, a modification of the classical Van der Pol oscillator is carried out by replacing the linear term x with the nonlinear term sinn (x) . The idea is to see the impact of the strength of this function on the appearance of chaotic dynamics for small and large values of the nonlinear dissipation term  . For this purpose, studies by numerical simulation and by analogue simulation are proposed. First, using nonlinear analysis tools, a similarity on the bifurcation sequences is observed despite a difference in the ranks of obtaining the particular behaviours and the bifurcation points. This study is confirmed by their respective maximum Lyapunov exponents. In a second step, a real implementation using microcontroller technology, which is motivated by the use of an artificial pacemaker, is carried out. For a more practical case, the excitation signal is generated by another microcontroller. The study shows a similarity with the results obtained numerically. Thirdly, in order to show that the model can be derived from mathematical modelling, an electronic simulation using OrCAD-Pspice software is also proposed. The results obtained are in qualitative agreement

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Section: Van Der Pol Model With Sinusoidal Non-linearitymentioning

confidence: 58%

Section: Introductionmentioning

confidence: 99%

Dynamical behavior analysis of the Van der Pol oscillator with sine nonlinearity subjected to non-sinusoidal periodic excitations by the bifurcation structures

et al. 2023

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“…One can quickly notice that the terms added in the current-voltage characteristic of the triode vacuum tube in this new model do not modify the Jacobian matrix of this oscillator around the equilibrium point [30]. Now, taking 1 e as a control parameter, one can evaluate the stability of the equilibrium point and its bifurcation according to [30]. The stability of the system can thus be obtained for 1 e satisfying the following relation:…”

Section: Fixed Point's Stability and Bifurcationmentioning

confidence: 98%

“…Bursting oscillation is one of the different types of oscillatory behavior observed in biological, physical, and chemical systems [30,[46][47][48][49]. It is characterized by the alternation of a silent phase and an active phase during each period of oscillation.…”

Section: Bursting Oscillationmentioning

confidence: 99%

On the modeling of some triodes-based nonlinear oscillators with complex dynamics: case of the Van der Pol oscillator

Tegnitsap¹,

Tsefack²,

Ngouonkadi³

et al. 2021

Phys. Scr.

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In this work, the dynamic of the triode-based Van der Pol oscillator coupled to a linear circuit is investigated (Triode-based VDPCL oscillator). Towards this end, we present a mathematical model of the triode, chosen from among the many different ones present in literature. The dynamical behavior of the system is investigated using classical tools such as two-parameter Lyapunov exponent, one-parameter bifurcation diagram associated with the graph of largest Lyapunov exponent, phase portraits, and time series. Numerical simulations reveal rather rich and complex phenomena including chaos, transient chaos, the coexistence of solutions, crisis, period-doubling followed by reverse period-doubling sequences (bubbles), and bursting oscillation. The coexistence of attractors is illustrated by the phase portraits and the cross-section of the basin of attraction. Such triode-based nonlinear oscillators can find their applications in many areas where ultra-high frequencies and high powers are demanded (radio, radar detection, satellites communication, etc.) since triode can work with these performances and are often used in the aforementioned areas. In contrast to some recent work on triode-based oscillators, LTSPICE simulations, based on real physical consideration of the triode, are carried out in order to validate the theoretical results obtained in this paper as well as the mathematical model adopted for the triode.

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“…Bursting dynamics [1,2], also called mixed-mode oscillations [3,4] or relaxation vibrations [5,6], created by the multi-time scale effect [7,8], is often observed in many nonlinear models, such as circuit oscillators [9,10], mechanical systems [11,12], nervous models [13,14] and chemical reactions [15,16]. Bursting oscillation is a complex dynamical behavior consisting of comparatively big-amplitude waves and approximately simple harmonic micro-amplitude vibrations, and is universally studied with the help of the slow/fast decomposition analysis that is proposed by in Rinzel [17] in 1985.…”

Section: Introductionmentioning

confidence: 99%

Intermittent bursting oscillations and the bifurcation analysis in an excited Rayleigh-Duffing oscillator

Zhang

Tang

Wang

2022

Preprint

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This paper investigates the bursting oscillations of a externally and parametrically forced Rayleigh-Duffing oscillator, in which three intermittent bursting types and one normal bursting type, namely intermittent “supHopf/supHopf-supHopf/supHopf” bursting, intermittent “fold/Homoclinic-Homoclinic/supHopf” bursting, intermittent “fold/Homoclinic-supHopf/supHopf” bursting and “fold/Homoclinic” bursting, are analyzed respectively. Recognizing the excitations as slow-varying state variables, the corresponding autonomous system can be exhibited and the bifurcation characteristics is briefly investigated, in particular, the Homoclinic bifurcation is analyzed by means of the Melnikov criterion. This paper shows that the dynamical behaviors of the excited Rayleigh-Duffing oscillator is touchy to the chosen of system parameters, different parameter conditions lead to distinct bifurcation structures that result in the trajectory approaching to different stable attractors and the appearance of different bursting forms. Our study increases the variousness of bursting oscillations and deepens the cognition of the generation mechanism of bursting dynamics. Lastly, the accuracy of the analysis presented in this paper is fully vindicated by the numerical simulations.

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Dynamical study of VDPCL oscillator: antimonotonicity, bursting oscillations, coexisting attractors and hardware experiments

Cited by 14 publications

References 36 publications

Dynamical behavior analysis of the Van der Pol oscillator with sine nonlinearity subjected to non-sinusoidal periodic excitations by the bifurcation structures

Dynamical behavior analysis of the Van der Pol oscillator with sine nonlinearity subjected to non-sinusoidal periodic excitations by the bifurcation structures

On the modeling of some triodes-based nonlinear oscillators with complex dynamics: case of the Van der Pol oscillator

Intermittent bursting oscillations and the bifurcation analysis in an excited Rayleigh-Duffing oscillator

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