Modelo matemático para la toma de decisiones con respecto a inversiones sostenibles

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dc.contributor.advisorOlivat Tost, Gerard
dc.contributor.advisorPeña, Carlos
dc.contributor.advisorAngulo García, Fabiola
dc.contributor.authorCholo Camargo, Ingrid Milena
dc.contributor.researchgroupPercepción y Control Inteligente (Pci)
dc.date.accessioned2025-09-09T13:34:47Z
dc.date.available2025-09-09T13:34:47Z
dc.date.issued2025
dc.descriptiongraficasspa
dc.description.abstractLo ideal en cualquier sociedad es poder tener una buena calidad de vida, usar los recursos de manera adecuada sin dañar el medio ambiente y asegurar que estos recursos sean suficientes para las futuras generaciones. Una herramienta muy útil que ayuda a modelar este tipo de situaciones para entender su dinámica, es el modelo matemático. Por ello, se propone un modelo matemático que estudie la interacción entre el hombre y los recursos naturales, con el objetivo de optimizar la gestión sostenible de los recursos naturales y el crecimiento poblacional, ya que, una adecuada administración del recurso reduce el riesgo de su desaparición. Se considera una población aislada con parámetros constante para simplificar el análisis. Se usan técnicas de análisis de estabilidad, bifurcaciones, teoría de viabilidad y control óptimo para identificar condiciones iniciales bajo las cuales se puede lograr un equilibrio sostenible. Además, conociendo la condición inicial del sistema y un umbral mínimo de personas, se han encontrado umbrales sostenibles del bosque que pueden mantenerse. También se ha identificado el umbral máximo sostenible del bosque y la manera de mantenerlo. Se ha demostrado que, si se cuenta con una reserva mínima de bosque y/o una actividad económica adicional, la utilidad máxima será mayor. Los hallazgos sirven como base para diseñar políticas públicas que promuevan el uso sostenible de los recursos en sectores como la agricultura, la pesca y la silvicultura, promoviendo la regeneración de los recursos y el bienestar de las comunidades (Texto tomado de la fuente)spa
dc.description.abstractThe ideal scenario in any society is to ensure a good quality of life, use resources efficiently without harming the environment, and guarantee their availability for future generations. A powerful tool for modeling such situations and understanding their dynamics is the mathematical model. Therefore, this work proposes a mathematical model that studies the interaction between humans and natural resources, with the objective of optimizing the sustainable management of natural resources and population growth, as proper resource management reduces the risk of depletion. The model considers an isolated population with constant parameters to simplify the analysis. Stability analysis, bifurcation theory, viability theory, and optimal control techniques are used to identify initial conditions under which a sustainable equilibrium can be achieved. Additionally, by knowing the system’s initial condition and a minimum population threshold, sustainable forest thresholds that can be maintained have been determined. The maximum sustainable forest threshold and the strategies to preserve it have also been identified. It has been demonstrated that having a minimum forest reserve and/or an additional economic activity leads to higher maximum utility. The findings serve as a basis for designing public policies that promote the sustainable use of resources in sectors such as agriculture, fisheries, and forestry, fostering resource regeneration and the well-being of communitieseng
dc.description.curricularareaEléctrica, Electrónica, Automatización Y Telecomunicaciones.Sede Manizales
dc.description.degreelevelDoctorado
dc.description.degreenameDoctor en Ingeniería
dc.description.researchareaSistemas Dinámicos, Desarrollo Sostenible
dc.format.extent119 páginas
dc.format.mimetypeapplication/pdf
dc.identifier.instnameUniversidad Nacional de Colombiaspa
dc.identifier.reponameRepositorio Institucional Universidad Nacional de Colombiaspa
dc.identifier.repourlhttps://repositorio.unal.edu.co/spa
dc.identifier.urihttps://repositorio.unal.edu.co/handle/unal/88661
dc.language.isospa
dc.publisherUniversida Nacional de Colombia
dc.publisher.branchUniversidad Nacional de Colombia - Sede Manizales
dc.publisher.facultyFacultad de Ingeniería y Arquitectura
dc.publisher.placeManizales, Colombia
dc.publisher.programManizales - Ingeniería y Arquitectura - Doctorado en Ingeniería - Automática
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dc.rights.accessrightsinfo:eu-repo/semantics/openAccess
dc.rights.licenseReconocimiento 4.0 Internacional
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/
dc.subject.armarcDecision making
dc.subject.ddc330 - Economía::333 - Economía de la tierra y de la energía
dc.subject.proposalSistemas dinámicosspa
dc.subject.proposalBifurcacionesspa
dc.subject.proposalTeoría de viabilidadspa
dc.subject.proposalTeoría de control óptimospa
dc.subject.proposalUmbrales sosteniblesspa
dc.subject.proposalDynamic systemseng
dc.subject.proposalBifurcations
dc.subject.proposalViability theoryeng
dc.subject.proposalOptimal control theoryeng
dc.subject.proposalSustainable thresholdseng
dc.subject.unescoDesarrollo sostenible
dc.subject.unescoSustainable development
dc.subject.unescoToma de decisiones
dc.titleModelo matemático para la toma de decisiones con respecto a inversiones sosteniblesspa
dc.title.translatedMathematical model for decision-making regarding sustainable investmentseng
dc.typeTrabajo de grado - Doctorado
dc.type.coarhttp://purl.org/coar/resource_type/c_db06
dc.type.coarversionhttp://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.contentText
dc.type.driverinfo:eu-repo/semantics/doctoralThesis
dc.type.versioninfo:eu-repo/semantics/acceptedVersion
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