Chaos of the Rayleigh–Duffing oscillator with a non-smooth periodic perturbation and harmonic excitation

Zhou, Liangqiang; Chen, Fangqi

doi:10.1016/j.matcom.2021.08.014

Cited by 12 publications

(8 citation statements)

References 25 publications

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“…Chaos widely exists in many areas, such as astronomy, quantum mechanics, economy and finance, weather, climate, network science, thermodynamics, chemistry, probabilistic mathematics, fluid mechanics and so on [1][2][3][4][5][6][7]. The study indicates that chaos has a very important application value in power system protection, flow dynamics, biomedicine, computer technique, information science, cryptology, communication engineering and so on [8].…”

Section: Introductionmentioning

confidence: 96%

Chaos Suppression of a Fractional-Order Modificatory Hybrid Optical Model via Two Different Control Techniques

Gao

et al. 2022

Fractal Fract

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In this current manuscript, we study a fractional-order modificatory hybrid optical model (FOMHO model). Experiments manifest that under appropriate parameter conditions, the fractional-order modificatory hybrid optical model will generate chaotic behavior. In order to eliminate the chaotic phenomenon of the (FOMHO model), we devise two different control techniques. First of all, a suitable delayed feedback controller is designed to control chaos in the (FOMHO model). A sufficient condition ensuring the stability and the occurrence of Hopf bifurcation of the fractional-order controlled modificatory hybrid optical model is set up. Next, a suitable delayed mixed controller which includes state feedback and parameter perturbation is designed to suppress chaos in the (FOMHO model). A sufficient criterion guaranteeing the stability and the onset of Hopf bifurcation of the fractional-order controlled modificatory hybrid optical model is derived. In the end, software simulations are implemented to verify the accuracy of the devised controllers. The acquired results of this manuscript are completely new and have extremely vital significance in suppressing chaos in physics. Furthermore, the exploration idea can also be utilized to control chaos in many other differential chaotic dynamical models.

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Section: Introductionmentioning

confidence: 96%

Chaos Suppression of a Fractional-Order Modificatory Hybrid Optical Model via Two Different Control Techniques

Gao

et al. 2022

Fractal Fract

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“…For instance, Zhou and Chen reported on the Rayleigh-Duffing oscillator with non-smooth periodic perturbation and harmonic excitation. [11] Gendelman et al studied a forced vibro-impact oscillator with Coulomb friction. [12] Licsko and Csernak investigated the chaotic motions of a simple dry-friction oscillator.…”

Section: Introductionmentioning

confidence: 99%

“…Zhou and Chen investigated the chaotic motions of the Rayleigh-Duffing oscillator. [11] In Ref. [16], Meleshenko et al reported conservative chaos in a simple os-cillatory system with non-smooth nonlinearity.…”

Section: Introductionmentioning

confidence: 99%

Dynamic modelling and chaos control for a thin plate oscillator using Bubnov–Galerkin integral method

Jiao

Wang

Jin³

et al. 2023

Chinese Phys. B

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The utilization of thin plate systems based on acoustic vibration holds significant importance in micro-nano manipulation and the exploration of nonlinear science. This paper focuses on the analysis of an actual thin plate system driven by acoustic wave signals. By combining the mechanical analysis of thin plate microelements with the Bubnov-Galerkin integral method, the governing equation for the forced vibration of a square thin plate is derived. Notably, the reaction force of the thin plate vibration system is defined as $f = \alpha \left| w \right|$, resembling Hooke's law. The energy function and energy level curve of the system are also analyzed. Subsequently, the amplitude-frequency response function of the thin plate oscillator is solved using the harmonic balance method. Through numerical simulations, the amplitude-frequency curves are analyzed for different vibration modes under the influence of various parameters. Furthermore, the paper demonstrates the occurrence of conservative chaotic motions in the thin plate oscillator using theoretical and numerical methods. Dynamics maps illustrating the system's states are presented to reveal the evolution laws of the system. By exploring the effects of force fields and system energy, the underlying mechanism of chaos is interpreted. Additionally, the phenomenon of chaos in the oscillator can be controlled through the method of velocity and displacement states feedback, which holds significance for engineering applications.

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“…Although Melnikov approach only provides an approximate result, it is still one of few techniques allowing analytical prediction of chaos occurrence. For IO deterministic and stochastic systems, there have been many research results on the application of Melnikov theory [30][31][32][33]. However, for FO dynamical systems, the application of Melnikov theory is still relatively rare.…”

Section: Introductionmentioning

confidence: 99%

Taming chaos in generalized Liénard systems by the fractional-order feedback based on Melnikov analysis

Huang

2023

Phys. Scr.

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The dynamical behavior of Liénard systems has always been a hot topic in nonlinear analysis. In the present study, a simple fractional-order feedback controller is put forward to tame chaos for a class of forced generalized Liénard systems. Adopting harmonic balance method, the first-order approximate equivalent integer-order system of the original fractional-order system is deduced. Then the criterion for taming chaos is established by employing the Melnikov approach. Duffing-Rayleigh chaotic oscillator is taken as an example to illustrate the validity of the proposed method. Firstly, the critical feedback intensity and differential order for taming chaos are obtained by the proposed criterion. Then, multiple numerical indicators such as phase portrait, time history plot, Lyapunov exponent and bifurcation diagram are provided to assist in analyzing theoretical results.

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Chaos of the Rayleigh–Duffing oscillator with a non-smooth periodic perturbation and harmonic excitation

Cited by 12 publications

References 25 publications

Chaos Suppression of a Fractional-Order Modificatory Hybrid Optical Model via Two Different Control Techniques

Chaos Suppression of a Fractional-Order Modificatory Hybrid Optical Model via Two Different Control Techniques

Dynamic modelling and chaos control for a thin plate oscillator using Bubnov–Galerkin integral method

Taming chaos in generalized Liénard systems by the fractional-order feedback based on Melnikov analysis

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