Finite volume and asymptotic methods for stochastic neuron models with correlated inputs |
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Authors: | Robert Rosenbaum Fabien Marpeau Jianfu Ma Aditya Barua Kre?imir Josi? |
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Affiliation: | 1. Department of Mathematics, University of Houston, Houston, USA 2. Department of Biology and Biochemistry, University of Houston, Houston, USA
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Abstract: | We consider a pair of stochastic integrate and fire neurons receiving correlated stochastic inputs. The evolution of this system can be described by the corresponding Fokker?CPlanck equation with non-trivial boundary conditions resulting from the refractory period and firing threshold. We propose a finite volume method that is orders of magnitude faster than the Monte Carlo methods traditionally used to model such systems. The resulting numerical approximations are proved to be accurate, nonnegative and integrate to 1. We also approximate the transient evolution of the system using an Ornstein?CUhlenbeck process, and use the result to examine the properties of the joint output of cell pairs. The results suggests that the joint output of a cell pair is most sensitive to changes in input variance, and less sensitive to changes in input mean and correlation. |
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