  In neuroscience, synaptic plasticity refers to the set of mechanisms driving
the dynamics of neuronal connections, called synapses and represented by a
scalar value, the synaptic weight. A Spike-Timing Dependent Plasticity (STDP)
rule is a biologically-based model representing the time evolution of the
synaptic weight as a functional of the past spiking activity of adjacent
neurons. A general mathematical framework has been introduced
in~arXiv:2010.08195.
  In this paper we develop and investigate a scaling approach of these models
based on several biological assumptions. Experiments show that long-term
synaptic plasticity evolves on a much slower timescale than the cellular
mechanisms driving the activity of neuronal cells, like their spiking activity
or the concentration of various chemical components created/suppressed by this
spiking activity. For this reason, a scaled version of the stochastic model
of~arXiv:2010.08195 is introduced and a limit theorem, an averaging principle,
is stated for a large class of plasticity kernels. A companion
paper~arXiv:2010.08790 is entirely devoted to the tightness properties used to
prove these convergence results.
  These averaging principles are used to study two important STDP models:
pair-based rules and calcium-based rules. Our results are compared with the
approximations of neuroscience STDP models. A class of discrete models of STDP
rules is also investigated for the analytical tractability of its limiting
dynamical system.
