Dinámica global de sistemas mutualistas

Abstract

This work is framed within the field of Dynamical Systems and we aim to continue the study of the stability of dynamical systems that we already started on the subjects of “AED” and “MOM”. In this text we investigate the existence of a Lyapunov function associated to a gradientlike system, semigroups or evolution processes. Because of that, a detailed study of Morse theory plays a central role. The applicability of the results explained here is exemplified by studyng the attractor of a three dimensional mutualistic model of two plants in competition and a pollinator with cooperative relation with plants. Also we compare the dynamical properties of the system in the absence of the pollinator. We observe how cooperation is a common fact to increase biodiversity. We also give mathematical evidence on how a cooperative species induces an increased biodiversity, even if the cooperative specie is driven to extinction. Due to this fact, we propose a change in the formulation model wich could explain this kind of phenomenon.