Cooperative behavior in a jump diffusion model for a simple network of spiking neurons

Abstract

The distribution of time intervals between successivespikes generated by a neuronal cell --the interspike intervals(ISI)-- may reveal interesting features of the underlyingdynamics. In this study we analyze the ISI sequence --thespike train-- generated by a simple network of neurons whose outputactivity is modeled by a jump-diffusion process. We prove that,when specific ranges of the involved parameters are chosen, it is possible toobserve multimodal ISI distributions which reveal that the modelednetwork fires with more than one single preferred time interval.Furthermore, the system exhibits resonance behavior, withmodulation of the spike timings by the noise intensity. We also show that inhibition helps the signal transmission between theunits of the simple network.

Keywords

• noisy leaky integrate and fire
• multimodality.
• first exit times
• ornsteinuhlenbeck process
• stochastic resonance
• preferred timeintervals