Bursting synchronization in networks with long-range coupling mediated by a diffusing chemical substance |
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Authors: | RL Viana AM BatistaCAS Batista JCA de PontesFA dos S Silva SR Lopes |
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Institution: | a Departamento de Física, Universidade Federal do Paraná, 81531-990 Curitiba, Paraná, Brazil b Departamento de Matemática e Estatística, Universidade Estadual de Ponta Grossa, 84032-900 Ponta Grossa, Paraná, Brazil c Coordenação de Automação Industrial, Universidade Tecnológica Federal do Paraná, 84016-210 Ponta Grossa, Paraná, Brazil |
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Abstract: | Many networks of physical and biological interest are characterized by a long-range coupling mediated by a chemical which diffuses through a medium in which oscillators are embedded. We considered a one-dimensional model for this effect for which the diffusion is fast enough so as to be implemented through a coupling whose intensity decays exponentially with the lattice distance. In particular, we analyzed the bursting synchronization of neurons described by two timescales (spiking and bursting activity), and coupled through such a long-range interaction network. One of the advantages of the model is that one can pass from a local (Laplacian) type of coupling to a global (all-to-all) one by varying a single parameter in the interaction term. We characterized bursting synchronization using an order parameter which undergoes a transition as the coupling parameters are changed through a critical value. We also investigated the role of an external time-periodic signal on the bursting synchronization properties of the network. We show potential applications in the control of pathological rhythms in biological neural networks. |
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Keywords: | Bursting neurons Bursting synchronization Neuronal networks |
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