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dc.contributor.authorDelshams Valdés, Amadeu
dc.contributor.authorGuillamon Grabolosa, Antoni
dc.contributor.authorHuguet Casades, Gemma
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.date.accessioned2019-01-16T10:13:56Z
dc.date.available2019-10-01T00:25:54Z
dc.date.issued2018-10-01
dc.identifier.citationDelshams, A., Guillamon, A., Huguet, G. Quasiperiodic perturbations of heteroclinic attractor networks. "Chaos : an interdisciplinary journal of nonlinear science", 1 Octubre 2018, vol. 28, núm. 10.
dc.identifier.issn1054-1500
dc.identifier.urihttp://hdl.handle.net/2117/126922
dc.description.abstractWe consider heteroclinic attractor networks motivated by models of competition between neural populations during binocular rivalry. We show that gamma distributions of dominance times observed experimentally in binocular rivalry and other forms of bistable perception, commonly explained by means of noise in the models, can be achieved with quasiperiodic perturbations. For this purpose, we present a methodology based on the separatrix map to model the dynamics close to heteroclinic networks with quasiperiodic perturbations. Our methodology unifies two different approaches, one based on Melnikov integrals and the other one based on variational equations. We apply it to two models: first, to the Duffing equation, which comes from the perturbation of a Hamiltonian system and, second, to a heteroclinic attractor network for binocular rivalry, for which we develop a suitable method based on Melnikov integrals for non-Hamiltonian systems. In both models, the perturbed system shows chaotic behavior, while dominance times achieve good agreement with gamma distributions. Moreover, the separatrix map provides a new (discrete) model for bistable perception which, in addition, replaces the numerical integration of time-continuous models and, consequently, reduces the computational cost and avoids numerical instabilities
dc.language.isoeng
dc.publisherInstitute of Physics (IOP)
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 Spain
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística
dc.subject.lcshHamiltonian systems
dc.titleQuasiperiodic perturbations of heteroclinic attractor networks
dc.typeArticle
dc.subject.lemacSistemes hamiltonians
dc.contributor.groupUniversitat Politècnica de Catalunya. SD - Sistemes Dinàmics de la UPC
dc.identifier.doi10.1063/1.5050081
dc.description.peerreviewedPeer Reviewed
dc.relation.publisherversionhttps://aip.scitation.org/doi/10.1063/1.5050081
dc.rights.accessOpen Access
local.identifier.drac23512065
dc.description.versionPostprint (author's final draft)
local.citation.authorDelshams, A.; Guillamon, A.; Huguet, G.
local.citation.publicationNameChaos : an interdisciplinary journal of nonlinear science
local.citation.volume28
local.citation.number10


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