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arXiv · 1109.3332

Bursting synchronization in networks with long-range coupling mediated by a diffusing chemical substance

R. L. Viana·A. M. Batista·C. A. S. Batista·J. C. A. de Pontes·F. A. dos S. Silva·S. R. Lopes
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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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R. L. Viana, A. M. Batista, C. A. S. Batista, J. C. A. de Pontes, F. A. dos S. Silva, S. R. Lopes. 2011-09-15. Bursting synchronization in networks with long-range coupling mediated by a diffusing chemical substance. https://doi.org/10.1016/j.cnsns.2011.11.016

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