Before revision:  To study the bursting dynamics of a network , we develop a new stochastic model based on synaptic properties that also accounts for afterhyperpolarization , which shapes the end of a burst. A stochastic perturbation of this system leads to a succession of bursts and interbursts and we characterize their durations using a three dimensional phase-space analysis and numerical simulations.
After revision:  To study the bursting dynamics of a network , we develop a new stochastic model based on synaptic properties that also accounts for afterhyperpolarization (AHP), which is a key component of IBI. The framework is a novel stochastic three dimensional dynamical system perturbed by noise: numerical simulations can reproduce a succession of bursts and interbursts and we characterize their durations using a three dimensional phase-space analysis and numerical simulations.