论文标题
重置的确切解决的捕食者猎物模型
An exactly solvable predator prey model with resetting
论文作者
论文摘要
我们研究了一个简单的扩散粒子（猎物）的模型，该模型在与一群扩散的捕食者中遇到时可能会灭亡或重置其原始位置。我们表明，之前的猎物的生存概率$ t $以$ \ sim t^{ - θ（p，γ）} $为代数，其中指数$θ$连续取决于模型的两个参数，$ p $ th $ p $表示A prey在与pery of apentator and $γ= d_A的可能性中生存的可能性（ $ d_b $分别是猎物和捕食者的扩散常数。我们还准确地计算了概率分布$ p（n | t_c）$的总数，直到捕获时间$ t_c $，并表明它表现出异常的大偏差表格$ p（n | t_c）\ sim t_c^{ - φ\ lest（\ frac {n} {\ ln} {\ ln t_c} $。速率函数$φ（z）$是明确计算的。数值模拟与我们的分析结果非常吻合。
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 $\sim t^{-θ(p, γ)}$ where the exponent $θ$ depends continuously on two parameters of the model, with $p$ denoting the probability that a prey survives upon encounter with a predator and $γ= D_A/(D_A+D_B)$ 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 $P(N|t_c)\sim t_c^{- Φ\left(\frac{N}{\ln t_c}=z\right)}$ for large $t_c$. The rate function $Φ(z)$ is computed explicitly. Numerical simulations are in excellent agreement with our analytical results.
