Dynamic response and bifurcation for Rayleigh-Liénard oscillator under multiplicative colored noise

Yue, Xiaole; Yu, Bei; Li, Yongge; Xu, Yong

doi:10.1016/j.chaos.2021.111744

Cited by 7 publications

(2 citation statements)

References 62 publications

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“…The coexistence of a chaotic attractorand a periodic attractor in this oscillator was demonstrated. In addition, the evolutionary processes of the transient and steady-state probability density functions of the response under multiplicative coloured noise were discussed using the generalized cell-mapping method [22]. Kaviya et al studied a parametrically and externally driven Rayleigh-Liénard hybrid model.…”

Section: Introductionmentioning

confidence: 99%

A modified perturbation method for global dynamic analysis of generalized mixed Rayleigh–Liénard oscillator with cubic and quintic nonlinearities

Li,

Hou,

Zhang

et al. 2024

Phys. Scr.

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Deriving analytical relationship between the system parameters and amplitude of the limit cycle is a meaningful and challenging task. Currently, numerous existing analytical approximate methods struggle to achieve this goal when expressions of restoring force or nonlinear damping is complicated. To overcome this shortcoming, this study proposes a modified generalized harmonic function perturbation method. Using the proposed method, a generalized mixed Rayleigh–Liénard oscillator with cubic and quintic nonlinearities was investigated. The analytical relationships between the system parameters and amplitude of the limit cycle, as well as the expression of its characteristic quantity, were derived. By employing these analytical relationships, the existence, stability, number, position, and amplitude of each limit cycle are quantitatively analysed. The homoclinic and heteroclinic bifurcations were also predicted using the above analytical relationships. Additionally, analytical approximate solutions for this oscillator were calculated using the proposed method. All results obtained in this study were subsequently confirmed numerically to demonstrate their feasibility and validity. Consequently, the proposed method can be considered an effective supplement to perturbation-based methods. This also implies that the work presented in this paper has a certain theoretical significance and application value in the research area of quantitative analysis methods for strongly nonlinear oscillators.

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Section: Introductionmentioning

confidence: 99%

A modified perturbation method for global dynamic analysis of generalized mixed Rayleigh–Liénard oscillator with cubic and quintic nonlinearities

Li,

Hou,

Zhang

et al. 2024

Phys. Scr.

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show abstract

“…Chen [11] studied the smooth response of a hard spring Duffing oscillator with fractional derivative damping under combined harmonic and broadband noise excitation, solved the corresponding Fokker-Planck-Kolmogorov (FPK) equation, and investigated the effect of the fractional order on the stochastic jump bifurcation of the system. In [12][13][14][15], the relationship between random perturbations in the form of multiplicative and additive Gaussian white noise, and the stochastic response of the corresponding system were discussed. In [16][17][18], the critical parameter conditions for the occurrence of the stochastic P-bifurcation of the system under the influence of noise for Duffing oscillators, and the jump and bifurcation phenomena of the steady-state response of the system under noise excitation were analyzed.…”

Section: Introductionmentioning

confidence: 99%

Analysis of stochastic P-bifurcation and critical flutter velocity parameter effects on a 3 degree of freedom wing

Huang

2023

Preprint

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In this study, we develop a stochastic nonlinear aerodynamic model for a three degree of freedom (3-DOF) wing with higher-order substructural nonlinearity in a two-dimensional flow field, applying high-dimensional and multi-stable system dimensionality reduction analysis methods to reduce system dimensionality. We obtain linear and nonlinear critical flutter velocities for the system to experience significant oscillations. We discuss the influence law of the nonlinear stiffness coefficient and stochastic disturbance parameters on the large critical flutter velocity of the system. We derive the probability density function of the steady-state response in three directions, that is, plunge, pitch, and control surface angle, by applying the stochastic averaging method, and analyze the influence law of structural parameters and stochastic airflow disturbance on the stochastic flutter behavior of the system in a two-dimensional flow field. We apply the stochastic P-bifurcation analysis method for high-dimensional multidimensional systems to study the stochastic P-bifurcation phenomenon of the steady-state response of a 3-DOF wing flutter system under stochastic disturbances.

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Stochastic analysis of a time-delayed viscoelastic energy harvester subjected to narrow-band noise

Yang

Zeng

Sun

et al. 2022

International Journal of Non-Linear Mechanics

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Dynamic response and bifurcation for Rayleigh-Liénard oscillator under multiplicative colored noise

Cited by 7 publications

References 62 publications

A modified perturbation method for global dynamic analysis of generalized mixed Rayleigh–Liénard oscillator with cubic and quintic nonlinearities

A modified perturbation method for global dynamic analysis of generalized mixed Rayleigh–Liénard oscillator with cubic and quintic nonlinearities

Analysis of stochastic P-bifurcation and critical flutter velocity parameter effects on a 3 degree of freedom wing

Stochastic analysis of a time-delayed viscoelastic energy harvester subjected to narrow-band noise

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