Transient and steady-state responses in a self-sustained oscillator with harmonic and bounded noise excitations

Yue, Xiaole; Xu, Wei; Wang, Liang; Zhou, Bingchang

doi:10.1016/j.probengmech.2012.06.001

Cited by 33 publications

(11 citation statements)

References 32 publications

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“…A similar phenomenon has been observed and studied for various dynamical models, in which an unstable limit cycle separates the basins of attraction of a stable equilibrium and a stable limit cycle [11][12][13].…”

Section: Introductionsupporting

confidence: 68%

Stabilizing stochastically-forced oscillation generators with hard excitement: a confidence-domain control approach

2013

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Abstract. In this paper, noise-induced destruction of self-sustained oscillations is studied for a stochastically-forced generator with hard excitement. The problem is to design a feedback regulator that can stabilize a limit cycle of the closed-loop system and to provide a required dispersion of the generated oscillations. The approach is based on the stochastic sensitivity function (SSF) technique and confidence domain method. A theory about the synthesis of assigned SSF is developed. For the case when this control problem is ill-posed, a regularization method is constructed. The effectiveness of the new method of confidence domain is demonstrated by stabilizing auto-oscillations in a randomly-forced generator with hard excitement.

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Section: Introductionsupporting

confidence: 68%

Stabilizing stochastically-forced oscillation generators with hard excitement: a confidence-domain control approach

2013

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“…The SCM method was first proposed by Hsu [29] to increase the computational efficiency of point mapping. Various improvements of the SCM method appeared and were applied to analyze the dynamical phenomena, such as bifurcation, stochastic response, first-passage problem [21,[30][31][32][33][34][35][36][37][38][39][40][41]. As the most important improvement, the GCM method can determine all the global properties including stable and unstable manifolds with the help of the digraph theory [36,41].…”

Section: Introductionmentioning

confidence: 99%

“…As the most important improvement, the GCM method can determine all the global properties including stable and unstable manifolds with the help of the digraph theory [36,41]. The transient and steady-state PDFs of the stochastic response can be obtained by the GCM method [37].…”

Section: Introductionmentioning

confidence: 99%

Probabilistic response of dynamical systems based on the global attractor with the compatible cell mapping method

Yue

et al. 2019

Physica A: Statistical Mechanics and its Applications

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A generalized compatible cell mapping (CCM) method is proposed in this paper to take advantages of the simple cell mapping (SCM) method, the generalized cell mapping (GCM) method together with a subdivision procedure. A coarse cell partition is first used to obtain a covering set of the global attractor. Then, a finer global attractor is obtained by the subdivision process. The probabilistic response of stochastic dynamic systems is obtained by the sparse matrix analysis algorithm applied to the covering set of the global attractor. Because the computational domain is the covering set of the global attractor rather than the whole state space, the numerical efficiency of the proposed method can be greatly improved as compared to the GCM. A three-dimensional and a four-dimensional dynamical system under Poisson white noise excitation are studied to demonstrate the effectiveness of the proposed method for the probabilistic response analysis. Monte Carlo simulations show a good agreement with the proposed method.

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“…As a new version of cell mapping method, it is not only effectively used to analyze the global properties and global bifurcations of nonlinear systems [20][21][22][23][24], but also a powerful tool to study the response analysis and stochastic bifurcation [25][26][27][28][29] of systems with random excitations. In Ref.…”

Section: Introductionmentioning

confidence: 99%

First-passage time statistics in a bistable system subject to Poisson white noise by the generalized cell mapping method

Han

Yue

et al. 2015

Communications in Nonlinear Science and Numerical Simulation

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Transient and steady-state responses in a self-sustained oscillator with harmonic and bounded noise excitations

Cited by 33 publications

References 32 publications

Stabilizing stochastically-forced oscillation generators with hard excitement: a confidence-domain control approach

Stabilizing stochastically-forced oscillation generators with hard excitement: a confidence-domain control approach

Probabilistic response of dynamical systems based on the global attractor with the compatible cell mapping method

First-passage time statistics in a bistable system subject to Poisson white noise by the generalized cell mapping method

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