Transient behavior of particle transport in a Brownian motor

Cai, Guoqiang; Lin, Y K

doi:10.1103/physreve.70.027104

Cited by 2 publications

(1 citation statement)

References 5 publications

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“…A generalization version of model ( 5) was proposed by Cai and Lin, [16] which is defined as follows:…”

Section: Improved Deterministic Modelmentioning

confidence: 99%

Stationary Response of Lotka—Volterra System with Real Noises

Liu¹,

Xu²,

Wei-Ting³

2013

Commun. Theor. Phys.

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A stochastic version of Lotka-Volterra model subjected to real noises is proposed and investigated. The approximate stationary probability densities for both predator and prey are obtained analytically. The original system is firstly transformed to a pair of Itô stochastic differential equations. The Itô formula is then carried out to obtain the Itô stochastic differential equation for the period orbit function. The orbit function is considered as slowly varying process under reasonable assumptions. By applying the stochastic averaging method to the orbit function in one period, the averaged Itô stochastic differential equation of the motion orbit and the corresponding Fokker-Planck equation are derived. The probability density functions of the two species are thus formulated. Finally, a classical real noise model is given as an example to show the proposed approximate method. The accuracy of the proposed procedure is verified by Monte Carlo simulation.

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“…A generalization version of model ( 5) was proposed by Cai and Lin, [16] which is defined as follows:…”

Section: Improved Deterministic Modelmentioning

confidence: 99%

Stationary Response of Lotka—Volterra System with Real Noises

Liu¹,

Xu²,

Wei-Ting³

2013

Commun. Theor. Phys.

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Information entropies and dynamics in the stochastic ecosystem of two competing species

Xie¹,

Cai²,

Xiao-Le³

et al. 2012

Acta Phys. Sin.

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Using the models of stochastic population dynamics, the competitions and interactions of interspecies and between species and the stochastic environment are studied. In this paper, the stochastic ecosystems (in Itô or Statonovich model) of two competing species are investigated through evaluating probability densities and information entropy fluxes and productions of two species. The formulas of entropy flux (i.e. expectation of divergence) and entropy production are educed for numerical calculations, through the corresponding Fokker-Planck equation with its condition and the definition of Shannon entropy. The nonlinear characteristics of entropy fluxes are captured and the relationships are found between the extremal points of entropy productions and the rapid transitions or bifurcations. The numerical results obtained with path integration method show that the probability densities and Shannon entropies of these two stochastic models (in Itô or Statonovich meaning) have the same evolutional tendency but with different points of extrema.

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Transient behavior of particle transport in a Brownian motor

Cited by 2 publications

References 5 publications

Stationary Response of Lotka—Volterra System with Real Noises

Stationary Response of Lotka—Volterra System with Real Noises

Information entropies and dynamics in the stochastic ecosystem of two competing species

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