@Article{NoetelFreiMacaSchi:2018:SeReMo,
author = "Noetel, J. and Freitas, Vander Lu{\'{\i}}s de Souza and Macau,
Elbert Einstein Nehrer and Schimansky-Geier, L.",
affiliation = "{Humboldt-University at Berlin} and {Instituto Nacional de
Pesquisas Espaciais (INPE)} and {Universidade Federal de S{\~a}o
Paulo (UNIFESP)} and {Humboldt-University at Berlin}",
title = "Search and return model for stochastic path integrators",
journal = "Chaos",
year = "2018",
volume = "28",
number = "10",
pages = "e106302",
month = "Oct.",
abstract = "We extend a recently introduced prototypical stochastic model
describing uniformly the search and return of objects looking for
new food sources around a given home. The model describes the
kinematic motion of the object with constant speed in two
dimensions. The angular dynamics is driven by noise and describes
a pursuit and escape behavior of the heading and the position
vectors. Pursuit behavior ensures the return to the home and the
escaping between the two vectors realizes exploration of space in
the vicinity of the given home. Noise is originated by
environmental influences and during decision making of the object.
We take symmetric \α-stable noise since such noise is
observed in experiments. We now investigate for the simplest
possible case, the consequences of limited knowledge of the
position angle of the home. We find that both noise type and noise
strength can significantly increase the probability of returning
to the home. First, we review shortly main findings of the model
presented in the former manuscript. These are the stationary
distance distribution of the noise driven conservative dynamics
and the observation of an optimal noise for finding new food
sources. Afterwards, we generalize the model by adding a constant
shift \γ within the interaction rule between the two
vectors. The latter might be created by a permanent uncertainty of
the correct home position. Nonvanishing shifts transform the
kinematics of the searcher to a dissipative dynamics. For the
latter, we discuss the novel deterministic properties and
calculate the stationary spatial distribution around the home.",
doi = "10.1063/1.5040108",
url = "http://dx.doi.org/10.1063/1.5040108",
issn = "1054-1500",
language = "en",
targetfile = "noetel_search.pdf",
urlaccessdate = "27 abr. 2024"
}