author = "Batista, Carlos Alberto Schnaider and Viana, Ricardo Luiz and 
                         Szezech Junior, Jos{\'e} Danilo and Batista, Antonio Marcos and 
                         Macau, Elbert Einstein Nehrer",
          affiliation = "{Universidade Federal do Paran{\'a} (UFPR)} and {Universidade 
                         Federal do Paran{\'a} (UFPR)} and {Universidade Estadual de Ponta 
                         Grossa (UEPG)} and {Universidade Estadual de Ponta Grossa (UEPG)} 
                         and {Instituto Nacional de Pesquisas Espaciais (INPE)}",
                title = "Synchronization of phase oscillators with coupling mediated by a 
                         diffusing substance",
                 year = "2016",
         organization = "International Conference on Nonlinear Science and Complexity, 6.",
             keywords = "complex networks, nonlinear dynamics and complex systems, 
                         synchronization in nonlinear systems.",
             abstract = "Networks of coupled phase oscillators have been extensively used 
                         in many physical and biological applications. A number of 
                         different coupling prescriptions has been studied, but most 
                         attention has been given to two types: local coupling, where each 
                         oscillator interacts with its nearest neighbors; and global 
                         coupling, where an oscillator is coupled to the mean field of all 
                         other oscillators regardless of their position. However, in many 
                         applications it turns out that an intermediate form of coupling 
                         would better describe the system, since each oscillator interacts 
                         with its neighbors but with a strength which depends on the mutual 
                         spatial distance. Such non-local couplings have been studied for a 
                         long time but recently it was recognized their importance in the 
                         production of chimera states. One of the interesting dynamical 
                         aspects to be studied in networks of non-locally coupled phase 
                         oscillators is synchronization, which is a universal phenomenon. A 
                         paradigmatic example of them is the synchronization of flashing 
                         fireflies, which interact by the emission of light pulses. Since 
                         the velocity of light is very large, the coupling effect is 
                         rapidly spread along the network and fireflies can flash in 
                         unison, producing an impressive phenomenon. On the other hand, 
                         emission of light pulses is not the only way oscillators can use 
                         to communicate among themselves. Another possibility is the 
                         emission and absorption of a chemical substance which diffuses in 
                         the medium containing the oscillators. A theory for describing 
                         such phenomena has been proposed by Kuramoto, and in the case of 
                         fast relaxation it amounts to an interaction which decays 
                         exponentially with the distance between oscillators. In this work 
                         we consider a model of point-like phase oscillators which interact 
                         according to this non-local coupling prescription. We investigate 
                         in what extent the frequency synchronization properties vary with 
                         the coupling parameters. It turns out that there is a 
                         synchronization transition with properties depending on both the 
                         coupling strength and range.",
  conference-location = "S{\~a}o Jos{\'e} dos Campos, SP",
      conference-year = "16-20 May",
             language = "en",
           targetfile = "batista_synchronization.pdf",
        urlaccessdate = "16 jan. 2021"