Estabilidad local para el modelo discreto Lotka-Volterra con competencia intraespecie

Abstract

This type work degree is developed based monograph Article DYNAMICS OF A DISCRETE MODEL Lotka-Volterra written by Qamar Din SpringerOpen published in the magazine with doi: 10.1186 / 1687-1847-2013-95, in which is studied the stability of the discrete Lotka-Volterra system with intra-species competition. The set of equations describing the constant struggle for survival between two species living in the same habitat, one being the food of the other, it is called Lotka-Volterra model or predator-prey. This dynamic system is made in order to mathematically represent interactions between two or more species and each alteration to model provides more tools to understand and analyze this dynamic. The proposed of Lotka and Volterra only took into account the species, in order to improve this, introduce definitions as the birth rate, mortality rate, level of saturation and other parameters for represent such situations as real as possible; such as the predator-prey model with intra-species competition in which there is a logistics term regarding members of the same population. This paper will develop the model as the theory develops. In Chapter 1 explains and analyzes the original model [1, 7, 8] and the model with competition intra-species [1], after is linearize the model [4], then with analysis of the eigenvalues is determined whether the equilibrium points can be stable or not [5] and the behavior of the equilibrium points is displayed by Plane for java [6]. At the end of the chapter is explains Euler's method [9] to be used then the discrete Lotka-Volterra model with competition intra-species, the target is get rational differences equations [10]. In Chapter 2 concepts and theorems necessary will be introduced to develop the theory of difference equations [2, 3]. Following, is linearized, is obtained and analyzed the fixed points of the discrete Lotka-Volterra model with intra-species competition. In chapter 3 using Geogebra some numerical simulations are made, [11]; and the behavior of the equilibrium points is displayed by Pplane for java [6].