Análisis cualitativo de sistemas de ecuaciones diferenciales: aplicaciones a modelos de Lotka-Volterra n-dimensionales

Abstract

This work shows The Lotka-Volterra systems like a continuation of the diferential equations studies we have seen in the subjects “AED” and “EDP”. We concentrate on the analysis of the global stability of Lotka-Volterra systems. Once the existence and uniqueness of solutions for these systems is proved, we develop sufficient condition for the associated adjacency matrix to assure the existence of a unique global stable stationary solutions. Finally, we study Lotka-Volterra mutualism models associated to complex networks in Ecology, for which our previous results hold.