Transitions in Oscillatory Dynamics of Two Connected Neurons with Excitatory Synapses

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It is shown that long term behavior of two connected Integrate- and- Fire neurons with excitatory synapses is determined by some fixed-points. In the case of equal synaptic weights four different dynamic phases are found. Between these phases there is a specific phase with a global attractor fixed-point, which is of interest from different viewpoints. Simulations support our analytic work. When synaptic weights are equal we observe no synchronization but with different weight we do observe an almost synchronous state. Simulations show that when there is only one non-trivial fixed-point the period of oscillations is stable against small changes in synaptic weights