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

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 M>N) 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.