Drunken robber, tipsy cop: First passage times, mobile traps, and Hopf bifurcations
arXiv:1410.1391
Abstract
For a random walk on a confined one-dimensional domain, we consider mean first passage times (MFPT) in the presence of a mobile trap. The question we address is whether a mobile trap can improve capture times over a stationary trap. We consider two scenarios: a randomly moving trap and an oscillating trap. In both cases, we find that a stationary trap actually performs better (in terms of reducing expected capture time) than a very slowly moving trap; however, a trap moving sufficiently fast performs better than a stationary trap. We explicitly compute the thresholds that separate the two regimes. In addition, we find a surprising relation between the oscillating trap problem and a moving-sink problem that describes reduced dynamics of a single spike in a certain regime of the Gray-Scott model. Namely, the above-mentioned threshold corresponds precisely to a Hopf bifurcation that induces oscillatory motion in the location of the spike. We use this correspondence to prove the uniqueness of the Hopf bifurcation.
arXiv comment14 pages, 5 figures
References in corpus (12)
- Intermittent search strategies
- Optimal search strategies for hidden targets
- Optimal target search on a fast folding polymer chain with volume exchange
- Survival of an evasive prey
- Searching fast for a target on a DNA without falling to traps
- Pascal Principle for Diffusion-Controlled Trapping Reactions
- Trapping Reactions with Randomly Moving Traps: Exact Asymptotic Results for Compact Exploration
- Survival probability of a diffusing particle in the presence of Poisson-distributed mobile traps
- Resonant activation in the presence of non-equilibrated baths
- Lattice theory of trapping reactions with mobile species
- Can a Lamb Reach a Haven Before Being Eaten by Diffusing Lions?
- Encounter times in overlapping domains: application to epidemic spread in a population of territorial animals