Modelos matemáticos de simulación del crecimiento poblacional de especies consideradas en aislamiento o en interacción
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Date
2024
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Universidad Nacional de Trujillo
Abstract
La idea central del presente trabajo consiste en estudiar la convivencia de dos especies de animales y luego formular un modelo matemático de los fenómenos que se susciten para realizar el presente trabajo; he tenido que utilizar ciertos nociones previas, llamémosle preliminares básicas tales como: nociones de un sistema controlado, criterios de cibernética, algunos criterios de ecología y nociones básicas de algebra lineal, ecuaciones diferenciales básicas, sistemas de ecuaciones diferenciales, criterios elementales de sistemas dinámicos lineales y planos, criterios básicos de estabilidad y conceptos de un modelo matemáticos. Con estos antecedentes, enfoco el tema central en el cual analizo e interpreto algunos modelos maten áticos que simulen el crecimiento o decrecimiento poblacional de especies. Para hacer los análisis uso los métodos inductivo y deductivo, e interpretación con visiones geométricas dinámicas, ecológicas, cibernéticas y con conocimiento de sistemas de control y así conseguir una expresión o modelo matemático que pueda predecir el futuro de las especies en estudio que podría ser útil en la ganadería o agricultura. Al final, informo el deseo alcanzado del trabajo de acuerdo a mi propósito deseado, mencionando algunas sugerencias que quizá sirvan para algunas investigaciones sobre temas relacionados al presente trabajo.
Abstract The central idea of this work is to study the coexistence of two species of animals and then to formulate a mathematical model of the phenomena that arise to carry out this work; I’ve had to use certain preconceptions, let’s call them basic preliminaries, such as: notions of a controlled system, criteria of cybernetics, some criteria of ecology and basic notions of linear algebra, basic differential equations, systems of differential equations, elementary criteria of linear and planic dynamical systems, basic criteria of stability and concepts of a mathematical model. With this background, I focus on the central topic in which I analyze and interpret some mathematical models that simulate the population growth or decrease of species. To make the analyses, I use the inductive and deductive methods, and interpretation with dynamic, ecological, cybernetic geometric visions and with knowledge of control systems and thus obtain an expression or mathematical model that can predict the future of the species under study that could be useful in livestock or agriculture. At the end, I report the desire achieved for the work according to my desired purpose, mentioning some suggestions that may be useful for some research on topics related to this work
Abstract The central idea of this work is to study the coexistence of two species of animals and then to formulate a mathematical model of the phenomena that arise to carry out this work; I’ve had to use certain preconceptions, let’s call them basic preliminaries, such as: notions of a controlled system, criteria of cybernetics, some criteria of ecology and basic notions of linear algebra, basic differential equations, systems of differential equations, elementary criteria of linear and planic dynamical systems, basic criteria of stability and concepts of a mathematical model. With this background, I focus on the central topic in which I analyze and interpret some mathematical models that simulate the population growth or decrease of species. To make the analyses, I use the inductive and deductive methods, and interpretation with dynamic, ecological, cybernetic geometric visions and with knowledge of control systems and thus obtain an expression or mathematical model that can predict the future of the species under study that could be useful in livestock or agriculture. At the end, I report the desire achieved for the work according to my desired purpose, mentioning some suggestions that may be useful for some research on topics related to this work
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Keywords
sistemas dinámicos, sistemas lieneales, modelos de crecimiento poblacional, modelo Lotka-Volterra.