  Spike time response curves (STRC's) are used to study the influence of
synaptic stimuli on the firing times of a neuron oscillator without the
assumption of weak coupling. They allow us to approximate the dynamics of
synchronous state in networks of neurons through a discrete map. Linearization
about the fixed point of the discrete map can then be used to predict the
stability of patterns of synchrony in the network. General theory for taking
into account the contribution from higher order STRC terms, in the
approximation of the discrete map for coupled neuronal oscillators in synchrony
is still lacking. Here we present a general framework to account for higher
order STRC corrections in the approximation of discrete map to determine the
domain of 1:1 phase locking state in the network of two interacting neurons. We
begin by demonstrating that the effect of synaptic stimuli through a shunting
synapse to a neuron firing in the gamma frequency band (20-80 Hz) last for
three consecutive firing cycles. We then show that the discrete map derived by
taking into account the higher order STRC contributions is successfully able
predict the domain of synchronous 1:1 phase locked state in a network of two
heterogeneous interneurons coupled through a shunting synapse.
