Gauss-diffusion processes for modeling the dynamics of a couple of interacting neurons.
With the aim to describe the interaction between a couple of neurons a stochastic model is proposed and formalized. In such a model, maintaining statements of the Leaky Integrate-and-Fire framework, we include a random component in the synaptic current, whose role is to modify the equilibrium point of the membrane potential of one of the two neurons and when a spike of the other one occurs it is turned on. The initial and after spike reset positions do not allow to identify the inter-spike intervals with the corresponding first passage times. However, we are able to apply some well-known results for the first passage time problem for the Ornstein-Uhlenbeck process in order to obtain (i) an approximation of the probability density function of the inter-spike intervals in one-way-type interaction and (ii) an approximation of the tail of the probability density function of the inter-spike intervals in the mutual interaction. Such an approximation is admissible for small instantaneous firing rates of both neurons.
Dipartimento di Matematica e Applicazioni "R. Caccioppoli", Universita di Napoli Federico II, Via Cintia, 80126 Napoli, Italy. aniello.buonocore@unina.it.
Aniello
A
Buonocore
Luigia
L
Caputo
Enrica
E
Pirozzi
Maria Francesca
MF
Carfora
D000200:Action Potentials / Q000502:physiology*; D006801:Humans; D008959:Models, Neurological; D009474:Neurons / Q000502:physiology*; D016011:Normal Distribution; D013269:Stochastic Processes; D013570:Synaptic Membranes / Q000502:physiology*