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dc.contributor.authorCañizo J.A.en_US
dc.contributor.authorYoldas H.en_US
dc.date.accessioned2019-01-07T13:14:20Z
dc.date.available2019-01-07T13:14:20Z
dc.date.issued2019-01-04
dc.identifier.issn1361-6544
dc.identifier.issn0951-7715
dc.identifier.urihttp://hdl.handle.net/20.500.11824/908
dc.description.abstractWe study two population models describing the dynamics of interacting neurons, initially proposed by Pakdaman et al (2010 Nonlinearity 23 55–75) and Pakdaman et al (2014 J. Math. Neurosci. 4 1–26). In the first model, the structuring variable s represents the time elapsed since its last discharge, while in the second one neurons exhibit a fatigue property and the structuring variable is a generic 'state'. We prove existence of solutions and steady states in the space of finite, nonnegative measures. Furthermore, we show that solutions converge to the equilibrium exponentially in time in the case of weak nonlinearity (i.e. weak connectivity). The main innovation is the use of Doeblin's theorem from probability in order to show the existence of a spectral gap property in the linear (no-connectivity) setting. Relaxation to the steady state for the nonlinear models is then proved by a constructive perturbation argument.en_US
dc.description.sponsorshipMTM2014-52056-P, MTM2017-85067-P, "la Caixa" Foundationen_US
dc.formatapplication/pdfen_US
dc.language.isoengen_US
dc.publisherNonlinearityen_US
dc.relationES/1PE/SEV-2013-0323en_US
dc.relationEUS/BERC/BERC.2014-2017en_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/es/en_US
dc.subjectstructured population dynamics, nonlinear asymptotic stability, neuron populations, Doeblin theoryen_US
dc.titleAsymptotic behaviour of neuron population models structured by elapsed-timeen_US
dc.typeinfo:eu-repo/semantics/articleen_US
dc.typeinfo:eu-repo/semantics/publishedVersionen_US
dc.identifier.doi10.1088/1361-6544/aaea9c
dc.relation.publisherversionhttp://iopscience.iop.org/article/10.1088/1361-6544/aaea9c/metaen_US


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