English

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

Chaotic Dynamics 2015-05-30 v1

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.

Keywords

Cite

@article{arxiv.1109.3332,
  title  = {Bursting synchronization in networks with long-range coupling mediated by a diffusing chemical substance},
  author = {R. L. Viana and A. M. Batista and C. A. S. Batista and J. C. A. de Pontes and F. A. dos S. Silva and S. R. Lopes},
  journal= {arXiv preprint arXiv:1109.3332},
  year   = {2015}
}

Comments

13 figures

R2 v1 2026-06-21T19:05:17.152Z