Análisis cualitativo para el modelo competitivo Lotka-Volterra en el plano
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Even without knowing the explicit solutions for a system of nonlinear differential equations, it is possible, through the use of the qualitative theory of dynamical systems, to study the behavior of those systems in neighborhoods of their equilibrium points and even more, to draw conclusions about its local and global stability. The main objective of this document is directed precisely in this sense, we study the qualitative behavior of the two-dimensional Lotka-Volterra system by analyzing the linearized system in neighborhoods of its equilibrium points, and by means of the link that exists between local and global stability for this type of systems, we draw conclusions about their global stability. And through the use of numerical simulations carried out in Python we graphically show the mathematical results obtained. Finally we establish an interpretation of these from the ecological point of view.