An exactly solvable predator prey model with resetting
| Autor: | Martin R Evans, Satya N Majumdar, Grégory Schehr |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: |
Statistics and Probability
Statistical Mechanics (cond-mat.stat-mech) diffusion General Physics and Astronomy FOS: Physical sciences Statistical and Nonlinear Physics Modeling and Simulation Condensed Matter::Superconductivity resetting Quantitative Biology::Populations and Evolution predator-prey model survival probability Condensed Matter - Statistical Mechanics Mathematical Physics 82C05 |
| Zdroj: | Evans, M R, Majumdar, S N & Schehr, G 2022, ' An exactly solvable predator prey model with resetting ', Journal of Physics A: Mathematical and Theoretical, vol. 55, no. 27, 274005, pp. 1-19 . https://doi.org/10.1088/1751-8121/ac7269 |
| DOI: | 10.1088/1751-8121/ac7269 |
| Popis: | 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 $\sim t^{-\theta(p, \gamma)}$ 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 $P(N|t_c)$ of the total number of encounters till the capture time $t_c$ and show that it exhibits an anomalous large deviation form $P(N|t_c)\sim t_c^{- \Phi\left(\frac{N}{\ln t_c}=z\right)}$ for large $t_c$. The rate function $\Phi(z)$ is computed explicitly. Numerical simulations are in excellent agreement with our analytical results. Comment: 18 pages, 3 figures, accepted for Journal of Physics A Special Issue "Stochastic Resetting: Theory and Applications" 2022 |
| Databáze: | OpenAIRE |
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