Independent variable time-step integration of individual neurons for network simulations

Realistic neural networks involve the coexistence of stiff, coupled, continuous differential equations arising from the integrations of individual neurons, with the discrete events with delays used for modeling synaptic connections. We present here an integration method, the local variable time-step method (Ivardt), that uses separate variable-step integrators for individual neurons in the network. Cells that are undergoing excitation tend to have small time steps, and cells that are at rest with little synaptic input tend to have large time steps. A synaptic input to a cell causes reinitialization of only that cell's integrator without affecting the integration of other cells. We illustrated the use of Ivardt on three models: a worst-case synchronizing mutual-inhibition model, a best-case synfire chain model, and a more realistic thalamocortical network model.