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Complexity as a measure of paths to regularity

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dc.contributor Edgardo Ugalde;0000-0003-4450-932X es_MX
dc.contributor.advisor Ugalde Saldaña, Edgardo es_MX
dc.contributor.author España Tinajero, Andrea Arlette es_MX
dc.coverage.spatial México. San luis Potosí. San Luis Potosí es_MX
dc.creator Andrea Arlette España;0000-0002-6569-7035 es_MX
dc.date.accessioned 2023-06-28T20:38:03Z
dc.date.available 2023-06-28T20:38:03Z
dc.date.issued 2023-06-28
dc.identifier.uri https://repositorioinstitucional.uaslp.mx/xmlui/handle/i/8309
dc.identifier.uri https://iopscience.iop.org/article/10.1088/1751-8121/acd03a es_MX
dc.description.abstract In this thesis, a way to quantify the synchronization of a system is introduced. It is made from a codification of the paths towards synchronization for synchronizing flows defined over a network. The collection of paths toward synchronization defines a combinatorial structure, called the transition diagram, the main object of study. The cardinality of this collection defines a measure of complexity which depends on the dimension of the system. The transition diagram corresponding to the Laplacian flow over the complete graph K_N and the complete bipartite graph K_{N,N} is described, through a coding: the feasible states by increasing functions, and the transitions between them by consecutive functions that follow certain rules. These results are applied to the Kuramoto flow (over the same graph) when a neighborhood close to the diagonal is considered. Furthermore, it generalizes to flows that are monotonic (that is, its coordinates and the differences of the coordinates maintain the order). It is presented as well some numerical and analytical results concerning the Laplacian and Kuramoto flows over the cycle graph C_N, and the ring lattice family C(N,k). In this case there are a different perspective, due to their no-monotonic behavior. es_MX
dc.description.sponsorship Beca Nacional CONACYT 722957 es_MX
dc.description.statementofresponsibility Investigadores es_MX
dc.language Inglés es_MX
dc.publisher Facultad de Ciencias es_MX
dc.relation.ispartof REPOSITORIO NACIONAL CONACYT es_MX
dc.relation.requires Paths towards synchronization: analytical treatment of completely connected networks, 2023. Artículo científico es_MX
dc.rights Acceso Abierto es_MX
dc.rights.uri http://creativecommons.org/licenses/by-nc-sa/4.0 es_MX
dc.subject Non-linearity es_MX
dc.subject Synchronization es_MX
dc.subject Laplacian es_MX
dc.subject Kuramoto model es_MX
dc.subject.other CIENCIAS FÍSICO MATEMATICAS Y CIENCIAS DE LA TIERRA es_MX
dc.title Complexity as a measure of paths to regularity es_MX
dc.title.alternative Complexité définie comme une mesure des chemins conduisant à une certaine notion de régularité. es_MX
dc.type Tesis de doctorado es_MX
dc.degree.name Doctorado en Ciencias Interdisciplinarias es_MX
dc.degree.department Facultad de Ciencias es_MX


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