Caos en l’ecologia

Abstract

En aquest treball ens endinsem al món dels sistemes dinàmics, tant continus com discrets, estudiant com evolucionen certs models matemàtics al llarg del temps. Veurem que, per alguns sistemes, variant una mica les condicions inicials, poden esdevenir resultats completament diferents. Aquest fenòmen s’anomena caos i és present, com veurem, en diversos models aplicats a l’ecologia o al clima. L’objectiu del projecte és entendre quins són els ingredients perquè hi hagi caos, com detectar-lo i com mesurar-lo.

In this work we delve into the world of dynamical systems, both continuous and discrete, studying how certain mathematical models evolve over time. We will see that, for some systems, by varying the initial conditions very little, they can turn into completely different results. This phenomenon is called chaos and is present, as we will see, in several models applied to ecology or climate. The aim of the project is to understand what are the ingredients for chaos, how to detect it and how to measure it.