An exactly solvable predator prey model with resetting

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 similar to 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))similar to t(c)(-phi(N/lntc=z)). The rate function phi(z) is computed explicitly. Numerical simulations are in excellent agreement with our analytical results.

Automated summary

In this study, we investigate the survival probability and encounter frequency distribution of a diffusing particle (prey) interacting with a swarm of diffusing predators. The results reveal that both the survival probability and encounter frequency distribution depend on the parameters of the model, and the numerical simulations agree well with the analytical results.