Examinando por Tema "Sistemas hamiltonianos"
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DocumentoAplicación del método de darboux en el análisis de integralidad de un sistema diferencial de tipo lotka-volterra(Universidad Tecnológica de Pereira, 2021) José Fabian , Valencia Parra ; Cárdenas Alzate, Pedro PabloIn this work we study the existence problem of the first integral for systems of differential equations of the form x˙ = f1(x, y, z) y˙ = f2(x, y, z) z˙ = f3(x, y, z), where f1, f2, f3 are polynomial functions. A method is applied to find integrability conditions at the origin; this method is known as the Darboux integrability method, which uses invariant algebraic curves in the construction of a first integral. As an application of this method we consider a Lotka-Volterra type differential system whose equations are given by: x˙ = −x(x + αy + βz) = P(x, y, z) y˙ = −y(βx + y + αz) = Q(x, y, z) z˙ = −z(αx + βy + z) = R(x, y, z), where α, β ∈ R and x, y, z represents the species interaction.