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 ∼ 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 ) ∼ t c − Φ N ln t c = z for large t c . The rate function Φ( z ) is computed explicitly. Numerical simulations are in excellent agreement with our analytical results.