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 {Instituto Nacional de Pesquisas 
                         Espaciais (INPE)} and {Humboldt University at Berlin}",
                title = "Optimal noise in a stochastic model for local search",
              journal = "Physical Review E",
                 year = "2018",
               volume = "98",
               number = "2",
                pages = "e022128",
                month = "Aug.",
             abstract = "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.",
                  doi = "10.1103/PhysRevE.98.022128",
                  url = "http://dx.doi.org/10.1103/PhysRevE.98.022128",
                 issn = "1539-3755",
             language = "en",
           targetfile = "noetel_optimal.pdf",
        urlaccessdate = "13 jun. 2021"