Search processes with stochastic resetting and multiple targets
File(s)
Published version
Author(s)
Bressloff, Paul C
Type
Journal Article
Abstract
Search processes with stochastic resetting provide a general theoretical framework for understanding a wide
range of naturally occurring phenomena. Most current models focus on the first-passage-time problem of finding
a single target in a given search domain. Here we use a renewal method to derive general expressions for the
splitting probabilities and conditional mean first passage times (MFPTs) in the case of multiple targets. Our
analysis also incorporates the effects of delays arising from finite return times and refractory periods. Carrying
out a small-r expansion, where r is the mean resetting rate, we obtain general conditions for when resetting
increases the splitting probability or reduces the conditional MFPT to a particular target. This also depends on
whether πtot = 1 or πtot < 1, where πtot is the probability that the particle is eventually absorbed by one of the
targets in the absence of resetting. We illustrate the theory by considering two distinct examples. The first consists
of an actin-rich cell filament (cytoneme) searching along a one-dimensional array of target cells, a problem for
which the splitting probabilities and MFPTs can be calculated explicitly. In particular, we highlight how the
resetting rate plays an important role in shaping the distribution of splitting probabilities along the array. The
second example involves a search process in a three-dimensional bounded domain containing a set of N small
interior targets. We use matched asymptotics and Green’s functions to determine the behavior of the splitting
probabilities and MFPTs in the small-r regime. In particular, we show that the splitting probabilities and MFPTs
depend on the “shape capacitance” of the targets.
range of naturally occurring phenomena. Most current models focus on the first-passage-time problem of finding
a single target in a given search domain. Here we use a renewal method to derive general expressions for the
splitting probabilities and conditional mean first passage times (MFPTs) in the case of multiple targets. Our
analysis also incorporates the effects of delays arising from finite return times and refractory periods. Carrying
out a small-r expansion, where r is the mean resetting rate, we obtain general conditions for when resetting
increases the splitting probability or reduces the conditional MFPT to a particular target. This also depends on
whether πtot = 1 or πtot < 1, where πtot is the probability that the particle is eventually absorbed by one of the
targets in the absence of resetting. We illustrate the theory by considering two distinct examples. The first consists
of an actin-rich cell filament (cytoneme) searching along a one-dimensional array of target cells, a problem for
which the splitting probabilities and MFPTs can be calculated explicitly. In particular, we highlight how the
resetting rate plays an important role in shaping the distribution of splitting probabilities along the array. The
second example involves a search process in a three-dimensional bounded domain containing a set of N small
interior targets. We use matched asymptotics and Green’s functions to determine the behavior of the splitting
probabilities and MFPTs in the small-r regime. In particular, we show that the splitting probabilities and MFPTs
depend on the “shape capacitance” of the targets.
Date Issued
2020-08
Date Acceptance
2020-07-22
Citation
Physical Review E, 2020, 102 (2)
ISSN
2470-0045
Publisher
American Physical Society (APS)
Journal / Book Title
Physical Review E
Volume
102
Issue
2
Copyright Statement
©2020 American Physical Society
Identifier
http://dx.doi.org/10.1103/physreve.102.022115
Publication Status
Published
Article Number
022115
Date Publish Online
2020-08-12