Melnikov Chaos in a Modified Rayleigh–Duffing Oscillator with ϕ6 Potential

Miwadinou, C. H.; Monwanou, A. V.; Hinvi, L. A.; Koukpémèdji, A. A.; Ainamon, Cyrille; Orou, J. B. Chabi

doi:10.1142/s0218127416500851

Cited by 27 publications

(14 citation statements)

References 28 publications

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“…The purpose of this article is to present the intermittent bursting. To that end, we choose an excited Rayleigh-Duffing oscillation [45] written as…”

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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“…The purpose of this article is to present the intermittent bursting. To that end, we choose an excited Rayleigh-Duffing oscillation [45] written as…”

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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“…In general, dynamic systems and nonlinear sciences constitute a large field of research, given their application in several fields: in mechanics, chemistry, quantum optics, astrophysics, hydrodynamics, electronics, biophysics, and so on . Much of the discussion in the physics and engineering literature concerning damped oscillations, linear and nonlinear damping in certain applied systems play an important role since they may be used to suppress large amplitude oscillations or various instabilities, and they can also be used as a control mechanism [26][27][28][29]. For example, Soliman and ompson in [27] and Miwadinou et al in [28,29] studied with considerable detail the effects of the damping level on the resonance response of the steady-state solutions and on the basin bifurcation patterns of the escape oscillator.…”

Section: Introductionmentioning

confidence: 99%

“…One of the techniques used for the analytical determination of chaos is the Melnikov method. It is often used to research and predict horseshoe chaos [21,26,29].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Dynamics of the Quadratic-Damping Helmholtz Oscillator

et al. 2020

Self Cite

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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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“…The basic physical sense of the Rayleigh-Duffing equation lies in the allowance for the dependence on the highest powers of the velocity in the dissipative coefficient and in the frequency for a classical oscillator. This equation which has nonlinear dissipative terms and parametric excitation term can be used to model some systems such as Brusselator, Selkov, rolling response, certain MEMS systems, El Ninosouthern oscillation... [4,11,12,13,14,15,16,17,18,19,20]. The paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

Hysteresis, Quasiperiodicity and Chaoticity in a Nonlinear Dissipative Hybrid Oscillator

Monwanou

Miwadinou²,

Ainamon³

et al. 2017

IJBAS

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Hysteresis, quasi-periodicity and chaoticity in a nonlinear dissipative hybrid oscillator are studied. The modified Rayleigh-Duffing oscillator is considered. We simultaneously take into account the new nonlinear cubic, pure quadratic and hybrid dissipative terms which modify the classical Rayleigh-Duffing oscillator. The influence of each of these new parameters on the dynamics of the oscillator has been seriously studied and interesting results are obtained. It is clear that each of these new dissipation terms can be used to control the dynamics of this oscillator. Some may be used to reduce or eliminate hysteresis, amplitude jump and resonance phenomena; others may accentuate them. Similarly, these new parameters can be used to impose on the systems modeled by this oscillator, a regular, quasi-periodic or even chaotic behavior according to their field of application. Thus, one of the original results obtained is the equation of the curve delimiting the zone of instabilities of the amplitudes of harmonic oscillations. This equation thus makes it possible to know the zone of amplitude permitted or of the amplitude jump for the systems and thus to control and predict the loss or gain of energy during this jump. Finally, the second stability of the oscillations of the system is studied as well as the influence of the dissipation parameters on this stability. It should be noted that the influence of some of these parameters depends on the simultaneous presence of these parameters.

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Melnikov Chaos in a Modified Rayleigh–Duffing Oscillator with ϕ6 Potential

Cited by 27 publications

References 28 publications

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

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

Nonlinear Dynamics of the Quadratic-Damping Helmholtz Oscillator

Hysteresis, Quasiperiodicity and Chaoticity in a Nonlinear Dissipative Hybrid Oscillator

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