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 = "13 jun. 2021"