Active spike transmission in the neuron model with a winding threshold manifold

Authors:
V. B. Kazantsev;A. S. Tchakoutio Nguetcho;S. Jacquir;S. Binczak;J. M. Bilbault
Affiliations:
Institute of Applied Physics of RAS, 46 Uljanov Street, 603950 Nizhny Novgorod, Russia;Laboratoire LE2I UMR CNRS 5158, Université de Bourgogne, BP 47870, 21078 Dijon Cedex, France and Departement des Sciences Physiques, Ecole Normale Superieure, de Maroua, Université de Ma ...;Laboratoire LE2I UMR CNRS 5158, Université de Bourgogne, BP 47870, 21078 Dijon Cedex, France;Laboratoire LE2I UMR CNRS 5158, Université de Bourgogne, BP 47870, 21078 Dijon Cedex, France;Laboratoire LE2I UMR CNRS 5158, Université de Bourgogne, BP 47870, 21078 Dijon Cedex, France
Venue:
Neurocomputing
Year:
2012

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Abstract

We analyze spiking responses of excitable neuron model with a winding threshold manifold on a pulse stimulation. The model is stimulated with external pulse stimuli and can generate nonlinear integrate-and-fire and resonant responses typical for excitable neuronal cells (all-or-none). In addition we show that for certain parameter range there is a possibility to trigger a spiking sequence with a finite number of spikes (a spiking message) in the response on a short stimulus pulse. So active transformation of N incoming pulses to M (with MN) outgoing spikes is possible. At the level of single neuron computations such property can provide an active ''spike source'' compensating ''spike dissipation'' due to the integrate-and-fire N to 1 response. We delineate the dynamical mechanism for the N to M transformation based on the winding threshold manifold in the neighborhood of big saddle loop bifurcation. Based on the theoretical predictions, a nonlinear electronic circuit is designed implementing the active transmission in physical conditions.