ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Ivanchenko M. V. Generation of bursts in ensembles of spiking neurons with nonlocal coupling. Izvestiya VUZ. Applied Nonlinear Dynamics, 2007, vol. 15, iss. 3, pp. 3-14. DOI: 10.18500/0869-6632-2007-15-3-3-14

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text PDF(Ru):
(downloads: 315)
Article type: 

Generation of bursts in ensembles of spiking neurons with nonlocal coupling

Ivanchenko Mihail Vasilevich, Lobachevsky State University of Nizhny Novgorod

A mechanism of collective generation of bursts in ensembles of spiking neurons with nonlocal excitatory coupling is studied. Three types of the network topology is considered: (a) chains with regular short-range nonlocal coupling, (b) chains with a small number of random long-range connections and dominating regular short-range ones, (c) random ensembles with a power law of node degree distribution. It is shown, that there exists a common mechanism of burst generation resulting from instability of synchronous slow spiking as the coupling strengthens, giving rise to fast repetitive spikes. Dependence upon parameters of the network is analyzed. The relevance of the obtained results to neuroscience is discussed.

Key words: 
  1. Nichols GJ, Martin AR, Wallas B, Fuchs AP. From Neuron to Brain. Moscow: Editorial URSS Publ.; 2003. 672 p.
  2. Marder E, Calabrese RL. Principles of rhythmic motor pattern generation. Physiol. Rev. 1996;76:687–717.
  3. Steriade M, McCormick DA, Sejnowski TJ. Thalamocortical oscillations in the sleeping and aroused brain. Science. 1993;262:679–685. DOI: 10.1126/science.8235588.
  4. Engel AK, Fries P, Singer W. Dynamic predictions: Oscillations and synchrony in top-down processing. Nat. Rev. Neurosci. 2001;2:704–716. DOI: 10.1038/35094565.
  5. Timofeev I, Steriade M. Neocortical seizures: Initiation, development and cessation. Neuroscience. 2004;123:299–336. DOI: 10.1016/j.neuroscience.2003.08.051.
  6. Rabinovich M, Volkovskii A, Lecanda P, Huerta R, Abarbanel HD, Laurent G. Dynamical encoding by networks of competing neuron groups: Winnerless competition. Phys. Rev. Lett. 2001;87:068102. DOI: 10.1103/PhysRevLett.87.068102.
  7. Levi R, Varona P, Arshavsky YI, Rabinovich MI, Selverston AI. The role of sensory network dynamics in generating a motor program. J. Neurosci. 2005;25:9807–9815. DOI: 10.1523/JNEUROSCI.2249-05.2005.
  8. Kazantsev VB, Nekorkin VI, Binczak S, Bilbault JM. Spiking patterns emerging from wave instabilities in a one-dimensional neural lattice. Phys. Rev. E. 2003;68:017201. DOI: 10.1103/PhysRevE.68.017201.
  9. Komendantov AO, Canavier CC. Electrical coupling between model midbrain dopamine neurons: Effects on firing pattern and synchrony. J. Neurophys. 2002;87:1526–1541. DOI: 10.1152/jn.00255.2001.
  10. Osipov GV, Ivanchenko MV, Kurth JS, Hu B. Synchronized chaotic intermittent and spiking behavior in coupled map chains. Phys. Rev. E. 2005;71:056209. DOI: 10.1103/PhysRevE.71.056209.
  11. Ivanchenko MV, Osipov GV, Shalfeev VD, Kurths J. Network mechanism for burst generation. Phys. Rev. Lett. 2007;98:108101. DOI: 10.1103/PhysRevLett.98.108101.
  12. Rulkov NF. Modeling of spiking-bursting neural behavior using two-dimensional map. Phys. Rev. E. 2002;65:041922. DOI: 10.1103/PhysRevE.65.041922.
  13. Rulkov NF, Timofeev I, Bazhenov M. Oscillations in large-scale cortical networks: Map-based model. J. Comp. Neuroscience. 2004;17:203–223. DOI: 10.1023/B:JCNS.0000037683.55688.7e.
  14. Pikovsky A, Rosenblum M, Kurts Yu. Synchronization: A fundamental nonlinear phenomenon. Moscow: Tehnosphera; 2003. 493 p.
  15. Kuramoto Y. Chemical Oscillations, Waves and Turbulence. Springer: Berlin; 1984.
  16. Watts DJ, Strogatz SH. Collective dynamics of «small-world» networks. Nature. 1998;393:440–442. DOI: 10.1038/30918.
  17. Strogatz SH. Exploring complex networks. Nature. 2001;410:268–276. DOI: 10.1038/35065725.
  18. Eguiluz VM, Chialvo DR, Cecchi GA, Baliki M, Apkarian AV. Scale-free brain functional networks. Phys. Rev. Lett. 2005;94:018102. DOI: 10.1103/PhysRevLett.94.018102.
Short text (in English):
(downloads: 97)