{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,23]],"date-time":"2026-09-23T17:43:47Z","timestamp":1790185427527,"version":"4.1.0"},"reference-count":48,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"6","funder":[{"DOI":"10.13039\/100015052","name":"Fondation de l'Ecole Normale Superieure","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100015052","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Appl. Math."],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>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 [P. Robert and G. Vignoud, SIAM. J. Appl. Math., 81 (2021), pp. 1821--1846]. 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 Robert and Vignoud [ SIAM. J. Appl. Math., 81 (2021), pp. 1821--1846] is introduced and a limit theorem, an averaging principle, is stated for a large class of plasticity kernels. A companion paper [P. Robert and G. Vignoud, J. Stat. Phys. 183 (2021), 47] 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.<\/jats:p>","DOI":"10.1137\/20m1382891","type":"journal-article","created":{"date-parts":[[2021,11,8]],"date-time":"2021-11-08T11:26:16Z","timestamp":1636370776000},"page":"2362-2386","source":"Crossref","is-referenced-by-count":8,"title":["Stochastic Models of Neural Synaptic Plasticity: A Scaling Approach"],"prefix":"10.1137","volume":"81","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8122-8880","authenticated-orcid":true,"given":"Philippe","family":"Robert","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4115-4017","authenticated-orcid":true,"given":"Ga\u00ebtan","family":"Vignoud","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2021,11,8]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1007\/s00422-012-0475-9"},{"key":"atypb2","doi-asserted-by":"crossref","unstructured":"A. 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Gerstner and W. M. Kistler,\n                      Spiking Neuron Models: Single Neurons, Populations, Plasticity\n                      , Cambridge University Press, Cambridge, UK, 2002.","DOI":"10.1017\/CBO9780511815706"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1002\/j.1538-7305.1960.tb01603.x"},{"key":"atypb20","doi-asserted-by":"crossref","unstructured":"M. Graupner and N. Brunel,\n                      Mechanisms of induction and maintenance of spike-timing dependent plasticity in biophysical synapse models\n                      , Front. Comput. Neurosci. (2010),https:\/\/doi.org\/10.3389\/fncom.2010.00136.","DOI":"10.3389\/fncom.2010.00136"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1109359109"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1523\/JNEUROSCI.0104-16.2016"},{"key":"atypb23","unstructured":"P. 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