Abstract
The synchronisation behaviour of a network of FitzHugh-Nagumo (FHN) oscillators are investigated. As the FHN units are meant to represent interneurons, only inhibitory chemical coupling is considered. Each unit receives synaptic-like input from a given fraction of the other units, randomly chosen. The synchronisation properties of the neuronal population are investigated against the coupling features (number of connections per neuron, synaptic current duration and coupling strength) and the network heterogeneity. Critical parameter values leading to the network synchronisation are found to exist.
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References
G. M. Gray and W. Singer, “Stimulus-specific neuronal oscillations in orientation columns of cat visual cortex”, Proc. Natl. Acad. Sci. USA,vol. 86, pp. 1698–1702, 1989.
W. J. Freeman, “Measurement of oscillatory responses to electrical stimulation in olfactory bulb of cat”, J. Neurophys., vol. 35, pp. 762–779, 1972.
M. A. Whittington, R. D. Traub, J. G. R. Jefferys, “Synchronised oscillations in interneuron networks driven by metabotropic gluttamate receptor activation”, Nature, vol. 373, pp. 612-615, 1995.
R. Galambos, S. Makeig, P. J. Talmachoff, “A 40 Hz auditory potential recorded from the human scalp” Proc. Natl. Acad. Sci. USA, vol. 78, pp. 2643–2647, 1981.
C. M. Gray, P. Koning, A. K. Engel and W. Singer, “Oscillatory responses in cat visual cortex exhibit inter-columnar synchronisation which reflects global stimulus properties”, Nature, vol. 338, pp. 334–337, 1989.
M. Galarreta and S. Hestrin, “A network of fast-spiking cells in the cortex connected by electrical synapses”, Nature, vol. 402, pp. 72–75, 1999.
J. R. Gibson, M. Belerlein, B. W. Connors, “Two networks of electrically coupled inhibitory neurons in neocortex”, Nature, vol. 402, pp. 75–79, 1999.
M. Thomson, “Neurotrasmission: chemical and electrical interneuron coupling”, Current Biology, vol. 10, pp. 110–112, 2000.
J. L. P. Velazquez and P. L. Carlen, “Gap junctions, synchrony and seizures”, Trend in Neuroscience, vol. 23, pp. 68–74, 2000.
X. J. Wang, J. Rinzel, “Alternating and synchronous rhythms in reciprocally inhibitor model neurons”, Neural Comput., vol. 4, pp. 84–97, 1992.
X. J. Wang, J. Rinzel, “Spindle rhythmicity in the reticularis thalami nucleus: synchronisation among mutually inhibitory neurons”, Neuroscience, vol. 53, pp. 899–904, 1993.
D. Hansel, G. Mato, C. Meunier, “Synchrony in excitatory neural networks”, Neural Comput., vol. 7, pp. 307–335, 1995.
C. van Vreeswijk, L. F. Abbott, G. B. Ermentrout, “When inhibition, not excitation synchronises neural firing”, J. Comput. Neurosci., vol. 1, pp. 313–322, 1995.
Fisahn, F. G. Pike, E. H. Buhl, O. Paulsen, “Cholinergic induction of network oscillations at 40 Hz in the hippocampus in vitro”, Nature, vol. 394, pp. 186–189, 1998.
L. S. Benardo, “Recruitment of GABAergic inhibition and synchronisation of inhibitory interneurons in rat neocoterx”, J. Neurophysiol., vol. 77, pp. 3134–3144, 1997.
R. A. FitzHugh, “Impulses and physiological states in theoretical models of nerve membrane”, Biophys. J., vol. 1, pp. 445–466, 1961.
S. Chillemi, M. Barbi, A. Di Garbo, “Synchronisation in a network of FHN units with synaptic-like coupling”, Lecture Notes in Computer Science 1606:230–239 (1999).
W. P. Welsh, E. J. Lang, I. Sugihara, R. R. Llinàs, “Dynamic organisation of motor control within the olivocerebellar system”, Nature, vol. 374, 453–457 (1995)
X. J. Wang, G. Buzsaki, “Gamma oscillation by synaptic inhibition in a hippocampal interneuronal network model“, J. of Neuroscience, vol. 16, 6402–6413 (1996).
Methods in neuronal modeling, edited by C. Koch and I. Segev, MIT press (1998)
J. A. White, C. C. Chow, J. Ritt, J. Soto-Trevino, N. Kopell, “Synchronisation and oscillatory dynamics in heterogeneous, mutually inhibited neurons“, J. Comput. Neurosci., vol. 5, 5–16 (1998).
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Chillemi, S., Barbi, M., Di Garbo, A. (2001). Synchronisation Mechanisms in Neuronal Networks. In: Mira, J., Prieto, A. (eds) Connectionist Models of Neurons, Learning Processes, and Artificial Intelligence. IWANN 2001. Lecture Notes in Computer Science, vol 2084. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45720-8_11
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DOI: https://doi.org/10.1007/3-540-45720-8_11
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