Nonlinear Fokker-Planck Equations

Frank, T. D.

doi:10.1007/b137680

Cited by 41 publications

(3 citation statements)

References 13 publications

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“…FPE is also used to solve first passage time problem, firing rate computation and estimation of moments of stochastic conductance's [21], [23]. Solution of Fokker-Planck equation highly depends on the boundary conditions [14]. FPE solution highly depends on initial conditions and boundary conditions.…”

Section: Svd For Lif Neuron With Edd Kernel Functionmentioning

confidence: 99%

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Information Processing in Neuron with Exponential Distributed Delay

Choudhary¹,

Bharti

2018

IJMLNCE

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Section: Svd For Lif Neuron With Edd Kernel Functionmentioning

confidence: 99%

“…The primary difference in both techniques is the point of approximation in the subtime interval. Ito technique uses left bound of sub-time interval whereas Stratanovich techniques uses mean of the left and right bounds of sub-time interval [14].…”

Section: Distributed Delay Framework Of Neuron Modelmentioning

confidence: 99%

Information Processing in Neuron with Exponential Distributed Delay

Choudhary¹,

Bharti

2018

IJMLNCE

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“…The coupling of particles through the constraint of total current gives rise to a variety of regimes ranging from Kramers type transition, oscillatory bimodal distribution, to unimodal distribution with increasing total current. Other examples of emergent behavior have also been observed through nonlocal interaction via moments of distribution [20] or globally coupling mean field parameters such as those in the synchronization of Kuramoto coupled oscillators [21]. Concerted behaviors observed in crowd and biological synchrony [22,23] and recently in Li-ion batteries [24] motivate further theoretical modeling.…”

Section: Introductionmentioning

confidence: 99%

Population dynamics of driven autocatalytic reactive mixtures

Zhao

Bazant

2019

Phys. Rev. E

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Motivated by the theory of reaction kinetics based on nonequilibrium thermodynamics [1] and the linear stability of driven reaction-diffusion[2], we apply the Fokker-Planck equation to describe the population dynamics of an ensemble of reactive particles in contact with a chemical reservoir. We illustrate the effect of autocatalysis on the population dynamics by comparing systems with identical thermodynamics yet different reaction kinetics. The dynamic phase behavior of the system may be entirely different from what its thermodynamics may suggest. By defining phase separation for a particle ensemble to be when the probability distribution is bimodal, we find that thermodynamic phase separation may be suppressed by autoinhibitory reactions, while autocatalysis enhances phase separation and in some cases induce the ensemble that consists of thermodynamically single-phase systems to segregate into two distinct populations, which we term fictitious phase separation. Asymmetric reaction kinetics also results in qualitatively different population dynamics upon reversing the reaction direction. In the limit of negligible fluctuations, we use method of characteristics and linearization to study the evolution of the standard deviation of concentration as well as the condition for phase separation, in good agreement with the full numerical solution. Applications are discussed to Li-ion batteries and in situ x-ray diffraction.arXiv:1901.05575v1 [physics.chem-ph]

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