Two-neurons network. I. Integrate and fire pacemaker models

The behavior of two pacemakers simulated by integrate and fire oscillators reciprocally connected by synapses is studied. The activation of each synapse produces a sudden potential shift in the post-synaptic neuron. Two sorts of behaviour may occur when at least one synapse is excitatory. Phase-locking occurs for almost every set of parameters, and given certain initial conditions. Repetitive patterns in indifferent equilibrium appear in the presence of a given set of parameters and certain other initial conditions. Quasi-periodic behaviour corresponds to almost every set of parameters when both synapses are inhibitory, although repetitive patterns of firing in indifferent equilibrium occassionally occur.