Intermittent pathways towards a dynamical target

TL;DR

This paper studies how intermittent search strategies improve the detection of a fluctuating, dynamical target on a lattice, using analytical models and simulations to compare effectiveness.

Contribution

It introduces a multistate continuous-time random walk model to analyze intermittent search strategies for dynamical targets, providing analytical and numerical insights.

Findings

Intermittent strategies enhance detection probability compared to single-state searches.

Analytical results for survival probability and target lifetime match Monte Carlo simulations.

Detection performance depends on target dynamics and walkers' transition probabilities.

Abstract

In this paper, we investigate the quest for a single target, that remains fixed in a lattice, by a set of independent walkers. The target exhibits a fluctuating behavior between trap and ordinary site of the lattice, whereas the walkers perform an intermittent kind of search strategy. Our searchers carry out their movements in one of two states between which they switch randomly. One of these states (the exploratory phase) is a symmetric nearest neighbor random walk and the other state (relocating phase) is a symmetric next-nearest neighbor random walk. By using the multistate continuous-time random-walk approach we are able to show that for dynamical targets, the intermittent strategy (despite the simplicity of the kinetics chosen for searching) improves detection, in comparison to displacements in a single state. We have obtained analytic results, that can be numerically evaluated, for the Survival Probability and for the Lifetime of the target. Thus, we have studied the dependence of these quantities both in terms of the transition probability that describes the dynamics of the target and in terms of the parameter that characterizes the walkers' intermittency. In addition to our analytical approach, we have implemented Monte Carlo simulations, finding excellent agreement between the theoretical--numerical results and simulations.