Emergence of oscillations in a model of weakly coupled two Bonhoeffer-van der Pol equations

The classical Ornstein-Uhlenbeck diffusion neuronal model is generalized by inclusion of a time-dependent input whose strength exponentially decreases in time. The behavior of the membrane potential is consequently seen to be modeled by a process whose mean and covariance classify it as Gaussian-Markov. The effect of the input on the neuronʹs firing characteristics is investigated by comparing the firing probability densities and distributions for such a process with the corresponding ones of the Ornstein-Uhlenbeck model. All numerical results are obtained by implementation of a recently developed computational method.