Non-Lévy stable random walk propagators for a non-Markovian walk with both superdiffusive and subdiffusive regimes

Silva, M.A.A. da; Rocha, E.C.; Cressoni, J. C.; Silva, L.R. da; Viswanathan, G. M.

doi:10.1016/j.physa.2019.122793

Cited by 7 publications

(3 citation statements)

References 8 publications

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“…Recently, a model based on the elephant random walk [14] with reinforcement exhibiting superdiffusion, diffusion and subdiffusion at the long time limit has been formulated in discrete time and space [15]. The model presented here is actually a generalization of the elephant random walk model [14,[16][17][18][19][20][21][22], a jump process, to a persistent random walk framework with finite velocity [2,23,24]. Using the persistent random walk framework is advantageous, as extensions such as reactions, chemosensitive movement and interactions between agents are established in the literature [25][26][27][28][29][30][31][32][33] and convenient to introduce.…”

Section: Introductionmentioning

confidence: 99%

Anomalous Stochastic Transport of Particles with Self-Reinforcement and Mittag–Leffler Distributed Rest Times

et al. 2021

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We introduce a persistent random walk model for the stochastic transport of particles involving self-reinforcement and a rest state with Mittag–Leffler distributed residence times. The model involves a system of hyperbolic partial differential equations with a non-local switching term described by the Riemann–Liouville derivative. From Monte Carlo simulations, we found that this model generates superdiffusion at intermediate times but reverts to subdiffusion in the long time asymptotic limit. To confirm this result, we derived the equation for the second moment and find that it is subdiffusive in the long time limit. Analyses of two simpler models are also included, which demonstrate the dominance of the Mittag–Leffler rest state leading to subdiffusion. The observation that transient superdiffusion occurs in an eventually subdiffusive system is a useful feature for applications in stochastic biological transport.

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Section: Introductionmentioning

confidence: 99%

Anomalous Stochastic Transport of Particles with Self-Reinforcement and Mittag–Leffler Distributed Rest Times

et al. 2021

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“…The model represented in (3) is actually a continuous space and time generalization of the elephant random walk [30][31][32][33][34][35][36], which is discrete in space and time. A limitation of (3) is that only active states were included in the model.…”

Section: Introductionmentioning

confidence: 99%

Superdiffusion in self-reinforcing run-and-tumble model with rests

Fedotov,

Han,

Ivanov

et al. 2021

Preprint

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This paper introduces a run-and-tumble model with self-reinforcing directionality and rests. We derive a single governing hyperbolic partial differential equation for the probability density of random walk position, from which we obtain the second moment in the long time limit. We find the criteria for the transition between superdiffusion and diffusion caused by the addition of a rest state. The emergence of superdiffusion depends on both the parameter representing the strength of self-reinforcement and the ratio between mean running and resting times. The mean running time must be at least 2/3 of the mean resting time for superdiffusion to be possible. Monte Carlo simulations validate this theoretical result. This work demonstrates the possibility of extending the telegrapher's (or Cattaneo) equation by adding self-reinforcing directionality so that superdiffusion occurs even when rests are introduced.

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“…A single model based on the elephant random walk [14] with reinforcement exhibiting superdiffusion, diffusion and subdiffusion in the long time limit has been formulated in discrete time and space [15]. The model presented here is actually a generalization of the elephant random walk [14,16,17,18,19,20,21], a jump process, to a persistent random walk framework with finite velocity [22,2,23]. Using the persistent random walk framework is advantageous as extensions such as reactions, chemosensitive movement and interactions between agents are established in literature [24,25,26,27,28,29,30,31,32] and convenient to introduce.…”

Section: Introductionmentioning

confidence: 99%

Anomalous stochastic transport of particles with self-reinforcement and Mittag-Leffler distributed rest times

Han,

Alexandrov,

Gavrilova

et al. 2021

Preprint

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We introduce a persistent random walk model for the stochastic transport of particles involving selfreinforcement and a rest state with Mittag-Leffler distributed residence times. The model involves a system of hyperbolic partial differential equations with a non-local switching term described by the Riemann-Liouville derivative. From Monte Carlo simulations, this model generates superdiffusion at intermediate times but reverts to subdiffusion in the long time asymptotic limit. To confirm this result, we derive the equation for the second moment and find that it is subdiffusive in the long time limit. Analyses of two simpler models are also included, which demonstrate the dominance of the Mittag-Leffler rest state leading to subdiffusion. The observation that transient superdiffusion occurs in an eventually subdiffusive system is a useful feature for application in stochastic biological transport.

show abstract

Non-Lévy stable random walk propagators for a non-Markovian walk with both superdiffusive and subdiffusive regimes

Cited by 7 publications

References 8 publications

Anomalous Stochastic Transport of Particles with Self-Reinforcement and Mittag–Leffler Distributed Rest Times

Anomalous Stochastic Transport of Particles with Self-Reinforcement and Mittag–Leffler Distributed Rest Times

Superdiffusion in self-reinforcing run-and-tumble model with rests

Anomalous stochastic transport of particles with self-reinforcement and Mittag-Leffler distributed rest times

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