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@InProceedings{BatistaViaSzeBatMac:2016:SyPhOs, 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" }

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