{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,26]],"date-time":"2026-09-26T13:35:33Z","timestamp":1790429733628,"version":"4.1.0"},"reference-count":40,"publisher":"AIP Publishing","issue":"10","funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["IRTG 1740"],"award-info":[{"award-number":["IRTG 1740"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001807","name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo","doi-asserted-by":"publisher","award":["2015\/50122-0"],"award-info":[{"award-number":["2015\/50122-0"]}],"id":[{"id":"10.13039\/501100001807","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001807","name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo","doi-asserted-by":"publisher","award":["2017\/04552-9"],"award-info":[{"award-number":["2017\/04552-9"]}],"id":[{"id":"10.13039\/501100001807","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2018,10,1]]},"abstract":"<jats:p>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 \u201cpursuit\u201d and \u201cescape\u201d 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 \u03b1-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 \u03b3 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.<\/jats:p>","DOI":"10.1063\/1.5040108","type":"journal-article","created":{"date-parts":[[2018,10,4]],"date-time":"2018-10-04T17:55:20Z","timestamp":1538675720000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":6,"title":["Search and return model for stochastic path integrators"],"prefix":"10.1063","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9188-7545","authenticated-orcid":false,"given":"J.","family":"Noetel","sequence":"first","affiliation":[{"name":"Department of Physics, Humboldt-University at Berlin 1 , Newtonstr. 15, D-12489 Berlin, Germany"},{"name":"National Institute for Space Research 2 , 12227-010 Sao Jose dos Campos, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7989-0816","authenticated-orcid":false,"given":"V. 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