An exactly solvable predator prey model with resetting. Evans, M. R., Majumdar, S. N., & Schehr, G. arXiv:2202.06138 [cond-mat], February, 2022. arXiv: 2202.06138![An exactly solvable predator prey model with resetting [link]](https://bibbase.org/img/filetypes/link.svg "link")
Paper abstract bibtex We study a simple model of a diffusing particle (the prey) that on encounter with one of a swarm of diffusing predators can either perish or be reset to its original position at the origin. We show that the survival probability of the prey up to time $t$ decays algebraically as ${\}sim t{\textasciicircum}\{-{\}theta(p, {\}gamma)\}$ where the exponent ${\}theta$ depends continuously on two parameters of the model, with $p$ denoting the probability that a prey survives upon encounter with a predator and ${\}gamma = D_A/(D_A+D_B)$ where $D_A$ and $D_B$ are the diffusion constants of the prey and the predator respectively. We also compute exactly the probability distribution $P(N{\textbar}t_c)$ of the total number of encounters till the capture time $t_c$ and show that it exhibits an anomalous large deviation form $P(N{\textbar}t_c){\}sim t_c{\textasciicircum}\{- {\}Phi{\}left({\}frac\{N\}\{{\}ln t_c\}=z{\}right)\}$ for large $t_c$. The rate function ${\}Phi(z)$ is computed explicitly. Numerical simulations are in excellent agreement with our analytical results.
@article{evans_exactly_2022,
title = {An exactly solvable predator prey model with resetting},
url = {http://arxiv.org/abs/2202.06138},
abstract = {We study a simple model of a diffusing particle (the prey) that on encounter with one of a swarm of diffusing predators can either perish or be reset to its original position at the origin. We show that the survival probability of the prey up to time \$t\$ decays algebraically as \${\textbackslash}sim t{\textasciicircum}\{-{\textbackslash}theta(p, {\textbackslash}gamma)\}\$ where the exponent \${\textbackslash}theta\$ depends continuously on two parameters of the model, with \$p\$ denoting the probability that a prey survives upon encounter with a predator and \${\textbackslash}gamma = D\_A/(D\_A+D\_B)\$ where \$D\_A\$ and \$D\_B\$ are the diffusion constants of the prey and the predator respectively. We also compute exactly the probability distribution \$P(N{\textbar}t\_c)\$ of the total number of encounters till the capture time \$t\_c\$ and show that it exhibits an anomalous large deviation form \$P(N{\textbar}t\_c){\textbackslash}sim t\_c{\textasciicircum}\{- {\textbackslash}Phi{\textbackslash}left({\textbackslash}frac\{N\}\{{\textbackslash}ln t\_c\}=z{\textbackslash}right)\}\$ for large \$t\_c\$. The rate function \${\textbackslash}Phi(z)\$ is computed explicitly. Numerical simulations are in excellent agreement with our analytical results.},
language = {en},
urldate = {2022-02-15},
journal = {arXiv:2202.06138 [cond-mat]},
author = {Evans, Martin R. and Majumdar, Satya N. and Schehr, Grégory},
month = feb,
year = {2022},
note = {arXiv: 2202.06138},
keywords = {unread},
}
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