Statistical characteristics of a nonlinear resonance system parametrically excited by a random force

Medvedev, S. Yu.; Muzychuk, O. V.

doi:10.1007/bf01034351

Cited by 2 publications

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“…which coincides with the results obtained previously in [19]. The corresponding amplitude distribution is depicted in figure 3.…”

Section: J Stat Mech (2016) 054036supporting

confidence: 91%

“…Substituting equations (32) in equations ( 17)- (19) we have in dynamics only one stable point A = 0 for linear system (α β = = 0) and for nonlinear one in the case α β < 8 2 . In the opposite case α β > 8 2 there are two stable points (focus and limit cycle)…”

Section: Probability Analysis Of Van Der Pol Oscillator With Negative...mentioning

confidence: 99%

“…22)does not coincide with the dynamical stable point A 0 (see equation(19)). Substituting equation(14) in equation (22) for the soft excitation regime (β = 0) of Van der Pol generator we obtain…”

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confidence: 99%

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Probabilistic characteristics of noisy Van der Pol type oscillator with nonlinear damping

Dubkov¹,

Litovsky²

2016

J. Stat. Mech.

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The exact Fokker–Planck equation for the joint probability distribution of amplitude and phase of a Van der Pol oscillator perturbed by both additive and multiplicative noise sources with arbitrary nonlinear damping is first derived by the method of functional splitting of averages. We truncate this equation in the usual manner using the smallness of the damping parameter and obtain a general expression for the stationary probability density function of oscillation amplitude, which is valid for any nonlinearity in the feedback loop of the oscillator. We analyze the dependence of this stationary solution on system parameters and intensities of noise sources for two different situations: (i) Van der Pol generator with soft and hard excitation regimes; (ii) Van der Pol oscillator with negative nonlinear damping. As shown, in the first case the probability distribution of amplitude demonstrates one characteristic maximum, which indicates the presence of a stable limit cycle in the system. The non-monotonic dependence of stationary probability density function on oscillation frequency is also detected. In the second case we examine separately three situations: linear oscillator with two noise sources, nonlinear oscillator with additive noise and nonlinear oscillator with frequency fluctuations. For the last two situations, noise-induced transitions in the system under consideration are found.

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“…which coincides with the results obtained previously in [19]. The corresponding amplitude distribution is depicted in figure 3.…”

Section: J Stat Mech (2016) 054036supporting

confidence: 91%

Section: Probability Analysis Of Van Der Pol Oscillator With Negative...mentioning

confidence: 99%

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Probabilistic characteristics of noisy Van der Pol type oscillator with nonlinear damping

Dubkov¹,

Litovsky²

2016

J. Stat. Mech.

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Statistical time-reversal symmetry and its physical applications

Dubkov

2010

Chemical Physics

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Statistical characteristics of a nonlinear resonance system parametrically excited by a random force

Cited by 2 publications

References 1 publication

Probabilistic characteristics of noisy Van der Pol type oscillator with nonlinear damping

Probabilistic characteristics of noisy Van der Pol type oscillator with nonlinear damping

Statistical time-reversal symmetry and its physical applications

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