Limit Cycles in Predator-Prey Models

• Autor: Puchuri Medina, Liliana
• Formato: artículo
• Fecha de Publicación: 2017
• Institución: Universidad Nacional de Trujillo
• Repositorio: Revistas - Universidad Nacional de Trujillo
• Lenguaje: español
• OAI Identifier: oai:ojs.revistas.unitru.edu.pe:article/1427
• Enlace del recurso: https://revistas.unitru.edu.pe/index.php/SSMM/article/view/1427
• Nivel de acceso: acceso abierto
• Materia: Limit Cycles; Centers; Hamiltonian Fields; Ciclos límites; centro; campos hamiltonianos

The classic Lotka-Volterra model belongs to a family of differential equations known as “Generalized Lotka-Volterra”, which is part of a classification of four models of quadratic fields with center. These models have been studied to address the Hilbert infinitesimal problem, which consists in determine the number of limit cycles of a perturbed hamiltonian system with center. In this work, we first present an alternative proof of the existence of centers in Lotka-Volterra predator-prey models. This new approach is based in algebraic equations given by Kapteyn, which arose to answer Poincaré’s problem for quadratic fields. In addition, using Hopf Bifurcation theorem, we proof that more realistic models, obtained by a non-linear perturbation of a classic Lotka-Volterra model, also possess limit cycles.