Statistical Dynamics of Vibroimpact Systems

Dimentberg, M. F.; Menyailov, A. I.

doi:10.1007/978-3-642-83334-2_5

Cited by 23 publications

(35 citation statements)

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“…By adding a random phase in the harmonic process, the stochastic process n(t) is called the randomized harmonic process. This randomized harmonic process was proposed independently by Dimentberg [1] and Wedig [11], and can be used to model a variety of random phenomena. It reduces to a pure sinusoidal signal when r = 0.…”

Section: Random Fluctuations In Both Source Terms and System Parametersmentioning

confidence: 99%

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Dynamical models of love with time-varying fluctuations

Wauer

Schwarzer

Cai

et al. 2007

Applied Mathematics and Computation

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Section: Random Fluctuations In Both Source Terms and System Parametersmentioning

confidence: 99%

“…1 This unusual approach was picked up by an Italian-Austrian group [3,5,6] for a serious try to model such relationships by simple mathematical models composed of ordinary differential equations but under a little more realistic circumstances. Recently another attempt [7] was made to explain also the dynamics of love triangles.…”

Section: Introductionmentioning

confidence: 99%

Dynamical models of love with time-varying fluctuations

Wauer

Schwarzer

Cai

et al. 2007

Applied Mathematics and Computation

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“…The the basic mechanisms and factors that are mostly affected by environmental fluctuations are the prey growth rate and predator death rate (Dimentberg, 1988;Maiti, Jana, & Samanta, 2007;Maiti & Samanta, 2005, 2006Wollkind, Collings, & Logan, 1988). …”

Section: The Stochastic Modelmentioning

confidence: 99%

Deterministic and stochastic analysis of a prey–predator model with herd behaviour in both

Maiti¹,

Sen

Samanta

2016

Systems Science & Control Engineering

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This paper aims to study the dynamical behaviours of a prey-predator system, where both the prey and predator show herd behaviours. Positivity, boundedness, stability of equilibrium points, et cetera, are discussed in deterministic environment. To incorporate the effect of fluctuating environment, we have perturbed the birth rate of prey species and death rate of predator species by Gaussian white noises. Then the resulting model is cultured by the method of statistical linearization to study the stability and non-equilibrium fluctuation of the populations in stochastic environment. Numerical simulations are carried out to validate our analytical findings. Implications of our analytical and numerical findings are discussed critically. ARTICLE HISTORY

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“…However, it has been shown in [11,12] that a stochastic excitation may also lead to the suppression of the oscillation amplitude. The steady state response amplitude A of a SDOF linear system x + 2γẋ + ω 2 x = a sin(Ωt), γ > 0,…”

Section: Introductionmentioning

confidence: 99%