Modelos de colonização e colapso

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Universidade Federal de Goiás


In this work a basic immigration process was investigated which starts with a single colony with a single individual at the origin of a homogeneous tree with the other empty vertices. The process colonies are established at the vertices of the graph and each one grows during a random time, according to a process of general counting until a disaster that annihilates part of the population occurs. After the collapse a random amount of individuals survives and attempts to establish, in a independent manner, new colonies in a neighboring vertices. After a time these formed colonies also suffer catastrophes and the process is repeated. It is important to emphasize that the time until the disaster of each colony is independent of the others. Here this general process was studied under two methods, Poisson growth with geometric catastrophe and Yule growth with binomial catastrophe. That is, in each colony the population grows following a Poisson (or Yule), process during a random time, considered here exponential, and soon after that time its size is reduced according to the geometric (or binomial) law. Conditions were analyzed in the set of parameters so that these processes survived and limits were established that were relevant for the probability of survival, the number of colonies generated during the process and the range of the colonies in relation to the initial point.



REZENDE, Bruna Luiza de Faria. Modelos de colonização e colapso. 2017. 86 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Goiás, Goiânia, 2017.