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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Optimal noise in a stochastic model for local search

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Noetel, J. [1] ; Freitas, V. L. S. [2] ; Macau, E. E. N. [2, 3] ; Schimansky-Geier, L. [1, 4]
Total Authors: 4
[1] Humboldt Univ, Inst Phys, Newtonstr 15, D-12489 Berlin - Germany
[2] Natl Inst Space Res, BR-12227010 Sao Jose Dos Campos, SP - Brazil
[3] Univ Fed Sao Paulo, BR-12247014 Sao Jose Dos Campos, SP - Brazil
[4] Humboldt Univ, Berlin Bernstein Ctr Computat Neurosci, Unter Linden 6, D-10099 Berlin - Germany
Total Affiliations: 4
Document type: Journal article
Source: Physical Review E; v. 98, n. 2 AUG 27 2018.
Web of Science Citations: 2

We develop a prototypical stochastic model for a local search around a given home. The stochastic dynamic model is motivated by experimental findings of the motion of a fruit fly around a given spot of food but will generally describe the local search behavior. The local search consists of a sequence of two epochs. In the first the searcher explores new space around the home, whereas it returns to the home during the second epoch. In the proposed two-dimensional model both tasks are described by the same stochastic dynamics. The searcher moves with constant speed and its angular dynamics is driven by a symmetric alpha-stable noise source. The latter stands for the uncertainty to decide the new direction of motion. The main ingredient of the model is the nonlinear interaction dynamics of the searcher with its home. In order to determine the new heading direction, the searcher has to know the actual angles of its position to the home and of the heading vector. A bound state to the home is realized by a permanent switch of a repulsive and attractive forcing of the heading direction from the position direction corresponding to search and return epochs. Our investigation elucidates the analytic tractability of the deterministic and stochastic dynamics. Noise transforms the conservative deterministic dynamics into a dissipative one of the moments. The noise enables a faster finding of a target distinct from the home with optimal intensity. This optimal situation is related to the noise-dependent relaxation time. It is uniquely defined for all alpha and distinguishes between the stochastic dynamics before and after its value. For times large compared to this, we derive the corresponding Smoluchowski equation and find diffusive spreading of the searcher in the space. We report on the qualitative agreement with the experimentally observed spatial distribution, noisy oscillatory return times, and spatial autocorrelation function of the fruit fly. However, as a result of its simplicity, the model aims to reproduce the local search behavior of other units during their exploration of surrounding space and their quasiperiodic return to a home. (AU)

FAPESP's process: 17/04552-9 - Synchronization and control of network of chaotic oscillator with applications to the control of mobile autonomous vehicles in formation movement
Grantee:Vander Luis de Souza Freitas
Support type: Scholarships in Brazil - Doctorate
FAPESP's process: 15/50122-0 - Dynamic phenomena in complex networks: basics and applications
Grantee:Elbert Einstein Nehrer Macau
Support type: Research Projects - Thematic Grants