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Journal Articles SIAM Journal on Applied Mathematics Year : 2021

Stochastic Models of Neural Plasticity: A Scaling Approach


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 [37]. 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 [37] is introduced and a limit theorem, an averaging principle, is stated for a large class of plasticity kernels. A companion paper [36] 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.


Dates and versions

hal-03256017 , version 1 (10-06-2021)



Philippe Robert, Gaëtan Vignoud. Stochastic Models of Neural Plasticity: A Scaling Approach. SIAM Journal on Applied Mathematics, 2021, 81 (6), pp.2362--2386. ⟨10.1137/20M1382891⟩. ⟨hal-03256017⟩
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