Search and return model for stochastic path integrators

Author(s)

Noetel, J. ^{[1, 2]} ; Freitas, V. L. S. ^[1] ; Macau, E. E. N. ^{[1, 3]} ; Schimansky-Geier, L. ^{[4, 2, 5]}

Affiliation

^[1] Natl Inst Space Res, BR-12227010 Sao Jose Dos Campos - Brazil

^[2] Humboldt Univ, Dept Phys, Newtonstr 15, D-12489 Berlin - Germany

^[3] Univ Fed Sao Paulo, BR-12247014 Sao Jose Dos Campos - Brazil

^[4] Ohio Univ, Dept Phys & Astron, Athens, OH 45701 - USA

^[5] Humboldt Univ, Berlin Bernstein Ctr Computat Neurosci, Unter Linden 6, D-10099 Berlin - Germany

• Document type: Journal article
• Source: Chaos; v. 28, n. 10 OCT 2018.
• Web of Science Citations: 3

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 alpha-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. 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. Published by AIP Publishing. (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 Opportunities: Scholarships in Brazil - Doctorate
• FAPESP's process: 15/50122-0 - Dynamic phenomena in complex networks: basics and applications
• Grantee: Elbert Einstein Nehrer Macau
• Support Opportunities: Research Projects - Thematic Grants