Modeling nonlinear dissipative chemical dynamics by a forced modified Van der Pol-Duffing oscillator with asymmetric potential: Chaotic behaviors predictions

Miwadinou, C. H.; Monwanou, A. V.; Yovogan, J.; Hinvi, L. A.; Tuwa, P.R. Nwagoum; Orou, J. B. Chabi

doi:10.1016/j.cjph.2018.03.033

Cited by 33 publications

(23 citation statements)

References 27 publications

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“…It has been noticed the presence of chaotic behaviors of this model [20]. Our main objective of the work is to limit the undesirable effects of external excitation by using the active control strategy.…”

Section: Model and Equation Of Oscillationsmentioning

confidence: 99%

“…When we assume that the sink of the product is a first order reaction and we base ourselves that the laws of mass action and conservation, we get after some mathematical transformations that the self-oscillations in some nonlinear chemical systems can be modelised by the following single second order differential equation [10]- [20]:…”

Section: Model and Equation Of Oscillationsmentioning

confidence: 99%

“…The nonlinear parameter β mark the difference between the oscillator equation Equation 7and the equation of classical Van der Pol-Duffing oscillator. Many dynamic behaviors are obtained when the system is subject to an external sinusoidal excitation [20] and in this case the dynamics of the model is modeled by the following equation:…”

Section: Model and Equation Of Oscillationsmentioning

confidence: 99%

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Active Control of Chaotic Oscillations in Nonlinear Chemical Dynamics

Olabodé¹,

Lamboni²,

Orou³

2019

JAMP

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This work studies the active control of chemical oscillations governed by a forced modified Van der Pol-Duffing oscillator. We considered the dynamics of nonlinear chemical systems subjected to an external sinusoidal excitation. The approximative solution to the first order of the modified Van der Pol-Duffing oscillator is found using the Lindstedt's perturbation method. The harmonic balance method is used to find the amplitudes of the oscillatory states of the system under control. The effects of the constraint parameter and the control parameter of the model on the amplitude of oscillations are presented. The effects of the active control on the behaviors of the model are analyzed and it appears that with the appropriate selection of the coupling parameter, the chaotic behavior of the model has given way to periodic movements. Numerical simulations are used to validate and complete the analytical results obtained.

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Section: Model and Equation Of Oscillationsmentioning

confidence: 99%

Section: Model and Equation Of Oscillationsmentioning

confidence: 99%

Section: Model and Equation Of Oscillationsmentioning

confidence: 99%

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Active Control of Chaotic Oscillations in Nonlinear Chemical Dynamics

Olabodé¹,

Lamboni²,

Orou³

2019

JAMP

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“…If M(τ 0 ) � 0 and dM/dτ 0 ≠ 0 for some τ 0 and some sets of parameters, then horseshoes exist, and chaos occurs [21][22][23][24][25]. Using this Melnikov criterion for the appearance of the intersection between the perturbed and unperturbed separatrixes, it is found that chaos appears when the following condition is satisfied:…”

Section: Horseshoe Chaosmentioning

confidence: 99%

“…e object of chaos theory is the study of nonlinear phenomena governed by simple and deterministic laws whose behavior under certain conditions becomes unpredictable. Since its discovery in the 20th century, chaos has been one of the most interesting for dynamic systems in areas such as physics, mathematics, chemistry, biochemistry, economics and finance, epidemiology, and engineering [19][20][21][22][23][24][25]. Depending on the field of study, it is sometimes useful or undesirable to the point where many researchers are interested in its prediction and/or control.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Dynamics of the Quadratic-Damping Helmholtz Oscillator

et al. 2020

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In this paper, the Helmholtz equation with quadratic damping themes is used for modeling the dynamics of a simple prey-predator system also called a simple Lotka–Volterra system. From the Helmholtz equation with quadratic damping themes obtained after modeling, the equilibrium points have been found, and their stability has been analyzed. Subsequently, the harmonic oscillations have been studied by the harmonic balance method, and the phenomena of resonance and hysteresis are observed. The primary and secondary resonances have been researched by the multiple-scale method, and the conditions of stability of the amplitudes of oscillations are determined. Chaos is detected analytically by the Melnikov method and numerically using the basin of attraction, the bifurcation diagram, the Lyapunov exponent, the phase portrait, and the Poincaré section. The effects of all the parameters of the system are analyzed in detail, and special emphasis is placed on the new parameters. Through this analysis, the complex phenomena such as hysteresis, bistability, amplitude jump, resonances, and chaos have been obtained. The control of the parameters and the necessary conditions to control the aforementioned phenomena have been found.

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Numerical verification of the orders of accuracy of truncated asymptotic expansion solutions to the van der Pol equation

Mungkasi

2020

J Math Chem

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Modeling nonlinear dissipative chemical dynamics by a forced modified Van der Pol-Duffing oscillator with asymmetric potential: Chaotic behaviors predictions

Cited by 33 publications

References 27 publications

Active Control of Chaotic Oscillations in Nonlinear Chemical Dynamics

Active Control of Chaotic Oscillations in Nonlinear Chemical Dynamics

Nonlinear Dynamics of the Quadratic-Damping Helmholtz Oscillator

Numerical verification of the orders of accuracy of truncated asymptotic expansion solutions to the van der Pol equation

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