Models of Synapses

The synapse is the connection between neurons.
A model of two connected neurons should include the synapse, but in, for example, a point model, the synapse is just modelled as a connection strength.
Some synapses are excitatory, some are inhibitory, and some are more effective than others.
The time that it takes for the "energy" to get across the synapse and how that energy is transmitted can be modelled in different ways.
One simple model is the exponential decay model.
Another common model is the alpha model, which initially increases rapidly, then decays.
From a computational point of view, these synapses are static.
If you fire a neuron today, and then again tomorrow, it will do the exact same thing.
Of course, the really interesting thing about the brain is that it learns.
Modelling this learning is typically done by changing the synaptic weight.