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• W25944761 abstract "En aquest treball es donen alguns models matematics que intenten capturar els trets fonamentals de la teoria de levolucio Darwinista. Aquests models tenen en compte, principalment, la seleccio natural i la mutacio, principis basics de la teoria de levolucio. Per a aixo, es considera una densitat de poblacio, u(t,x), on x_[0,1]n denota una col·leccio de variables evolutives, es a dir, caracteristiques dels individus de la poblacio que poden mutar al reproduir-se (per exemple, el color) i es donen unes equacions que ens permetran calcular levolucio daquesta densitat de poblacio a mida que passa el temps.Al Capitol 1 es fa una introduccio dels models que ja existien a la literatura i dels que sintrodueixen a la memoria.Al Capitol 2 es considera una poblacio formada per individus que comparteixen les mateixes caracteristiques evolutives, es donen unes equacions amb retard en el temps modelant aquesta poblacio i sestudia primer lexistencia, unicitat i positivitat global de solucions. Despres es passa a estudiar lexistencia de solucions estacionaries i la seva estabilitat (local). Tambe sestudien alguns aspectes de la dinamica global com pot ser lexistencia datractors globals. Finalment, sestudien les estrategies evolutivament estables (ESS), es dona un esquema numeric Adams-Bashforth-Moulton i es fan unes simulacions numeriques.Al Capitol 3 es considera una poblacio dindividus com la del capitol anterior i es suposa que una proporcio daquesta ha adquirit una (o mes) caracteristica evolutiva que li permet explotar un nou recurs. Considerem doncs, dues densitats de poblacio: la dels ancestrals, u(t,x), i la dels mutants, v(t,x,y). Una vegada introduida la situacio es passa a donar un model matematic i veure que esta ben posat, es a dir, sestudia lexistencia, unicitat i positivitat global de solucions. Tambe sestudia lexistencia de solucions estacionaries aixi com la seva estabilitat local. Acte seguit es passa a estudiar alguns aspectes de la dinamica global.A lultim capitol es dona un model presa-predador i se suposa que la poblacio de preses depen dunes determinades variables evolutives. Com a la resta dels capitols comencem veient que el model donat esta ben posat, calculem lexistencia de solucions estacionaries i estudiem lestabilitat daquestes unicament en un cas particular. Donem lexistencia dun atractor global i calculem les estrategies evolutivament estables.In this work we give some mathematical models that try to capture the main traits of the darwinian theory of evolution. These models take into account mainly natural selection and mutation, which are the basic principles of the Theory of Evolution. In order to do that we consider the population density u(t,x), where x[0,1]n denotes a collection of evolutive variables, that is, characteristics of the individuals of the population that can mutate when reproducing (for instance, the color) and the equations that allow the prediction of this population density with time are given.In Chapter 1 we give an introduction to the already existing models in the literature and to the ones which are introduced in this work.In Chapter 2 we consider a population consisting of individuals sharing the same evolutive characteristics. We give the time lag equations modeling the evolution of this population and the global existence, uniqueness and positivity of the solutions are studied. Then we study the existence of stationary solutions and their (local) stability. We study also some aspects of their global dynamics, as the existence of global attractors. Finally the evolutionarily stable strategies (ESS) are studied, an Adams-Bashforth-Moulton method scheme is given and some numerical simulations are performed.In Chapter 3 we consider a population like the one considered in the previous chapter, when a certain number of their individuals have acquired one (or more) evolutive characteristics that allows them to exploit a new resource. Two population densities are hence considered: the ancestral one u(t,x) and the mutants v(t,x,y). Once this situation is established a mathematical model is given and shown to be well posed, that is, the global existence, uniqueness and positivity of solutions is studied. Next the existence of stationary solutions is considered, with the study of their local stability. Then some aspects of the global dynamics are established.In the last chapter a prey-predator model is given and it is assumed that the prey population depends on some determined evolutive variables. As in the preceding chapters, it is established that the model is well posed, the stationary solutions are determined and their stability is established in a particular case. The existence of a global attractor is proven and the evolutionarily stable strategies are computed." @default.
• W25944761 created "2016-06-24" @default.
• W25944761 creator A5040346449 @default.
• W25944761 date "2003-01-08" @default.
• W25944761 modified "2023-09-24" @default.
• W25944761 title "Modelització matemàtica d'alguns aspectes de la teoria de l'evolució Darwinista" @default.
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