DOI:
https://doi.org/10.14483/22484728.265Publicado:
2010-12-12Número:
Vol. 4 Núm. 2 (2010)Sección:
Visión InvestigadoraAnálogo estocástico del modelo Lotka-Volterra
Stochastic analog Lotka-Volterra model
Palabras clave:
population dynamics, Allee´s effect, LotkaVolterra model, system of differential equations, Itô formula, stochastic differential equations (en).Palabras clave:
dinámica poblacional, efecto Allee, modelo Lotka-Volterra, sistema de ecuaciones diferenciales, fórmula de Itô, ecuaciones diferenciales estocásticas (es).Descargas
Resumen (es)
La biomatemática o biología matemática es el estudio de fenómenos biológicos mediante herramientas matemáticas de diversa complejidad. Para modelarlos y analizarlos se usan ecuaciones diferenciales ordinarias, ecuaciones diferenciales parciales y/o ecuaciones diferenciales estocásticas. En este tópico interesa investigar la evolución de las especies y la relación con su ambiente (depredación, competencia, presencia y calidad del alimento, simbiosis y mutualismo, etc.), para predecir la evolución futura de los ecosistemas, sometidos a ciertas condiciones, e introducir técnicas de control en estos. En este artículo nos enfocaremos en presentar la versión determinista y estocástica de una variante del modelo Lotka-Volterra depredadorpresa para dos poblaciones, consistente en el sistema de ecuaciones diferenciales simultáneas, donde x e y representan el número de presas y predadores, respectivamente, con A, B, C, D constantes positivas que reflejan las condiciones de crecimiento de las especies y sus interacciones. El estudio de estos temas resulta ser de importancia en áreas como: el manejo de recursos renovables, la evolución de variedades resistentes a pesticidas, los fenómenos de sustitución tecnológica, el cambio organizativo o el aprendizaje organizativo.
Resumen (en)
The Biomathematics or Mathematics Biology is the study of biological phenomena using mathematical tools of varying complexity. For modeling and analyzing are ordinary differential equations, partial differential equations and / or stochastic differential equations. In this area, interested in investigating the evolution of species and the relationship with their environment (predation, competition, presence and quality of food, symbiosis and mutualism, etc.), To predict the future evolution of the ecosystems under certain conditions, introduce techniques to control them. In this article, we focus on the present version of a variant the model deterministic and stochastic LotkaVolterra predator-prey, two populations, consisting of the simultaneous differential equations system, where x and y represent the number of prey and predators, respectively, with A, B, C, D positive constants, which reflect the growing conditions of species and their interactions. The study of these issues appears to be of great importance in areas such as renewable resource management, development of varieties resistant to pesticides, technology substitution phenomena, organizational change or organizational learning.
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