2021
DOI: 10.1515/ijnsns-2019-0031
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Abstract: In this paper, nonlinear dynamics study of a RLC series circuit modeled by a generalized Van der Pol oscillator is investigated. After establishing a new general class of nonlinear ordinary differential equation, a forced Van der Pol oscillator subjected to an inertial nonlinearity is derived. According to the external excitation strength, harmonic, subharmonic and superharmonic oscillatory states are obtained using the multiple time scales method. Bifurcation diagrams displayed by the model for each system pa… Show more

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Cited by 8 publications
(3 citation statements)
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“…We can now describe the oscillations in terms of deviations from the equilibrium points. For such a deviation of the slow motion of X with respect to X å , introducing of the change of variable Y = X − X å into equation (11) and taking into account equation (13) lead after some mathematical manipulations to the following equation:…”
Section: Theoretical Analysis Of the Vibrational Resonancementioning
confidence: 99%
See 1 more Smart Citation
“…We can now describe the oscillations in terms of deviations from the equilibrium points. For such a deviation of the slow motion of X with respect to X å , introducing of the change of variable Y = X − X å into equation (11) and taking into account equation (13) lead after some mathematical manipulations to the following equation:…”
Section: Theoretical Analysis Of the Vibrational Resonancementioning
confidence: 99%
“…Due to their interesting dynamic behavior and its great potential applications, parametrically excited systems have attracted many attentions in the past. To that end, several works of different complexities have been performed on parametrically excited stiffness systems and interesting results have been obtained [6][7][8][9][10][11]. Contrary to parametric systems with time-varying stiffness, the parametric damping excitation is very few studied in the open literature.…”
Section: Introductionmentioning
confidence: 99%
“…As the van der Pol oscillator is easily implemented as a circuit, there have been many different types of experimental circuit models as well. These including circuits using vacuum tubes [9], operational amplifiers [10], resistor-inductor-capacitor [11], memristors [12], field programmable gate arrays [13], and field programmable analog arrays (FPAAs) [14]. In part because of its ability to be constructed as a circuit, the chaotic behavior of the van der Pol oscillator has been studied extensively [15][16][17][18].…”
Section: Introductionmentioning
confidence: 99%