Stability criterion for a two-neuron reciprocally coupled network based on the phase and burst resetting curves

Previously, we have used open-loop-phase resetting curves (PRCs) that were tabulated for postsynaptic neurons using a perturbation equal to a burst in the presynaptic neuron to predict the patterns exhibited by a closed-loop circuit containing these bursting neurons. This requires the assumption that the phase resetting observed in the circuit is the same with or without the feedback that occurs in a closed circuit, yet both the duration and waveform of the bursts can change under these conditions. Experimental and theoretical studies have shown that the amount of phase resetting produced in a neural oscillator by a synaptic input depends not only on the stimulus timing (phase), but also on its intensity and duration. The effects of variations in the synaptic coupling due to the waveform of the burst envelope or changes in frequency were ignored here, but the effects of the burst duration were incorporated into the stability analysis by tabulating the burst resetting curve (BRC) as a function of the phase of the presynaptic input in the open-loop condition.