Transcritical Bifurcations and Algebraic Aspects of Quadratic Multiparametric Families

Abstract

This article reveals an analysis of the quadratic systems that hold multiparametric families therefore, in the first instance the quadratic systems are identified and classified in order to facilitate their study and then the stability of the critical points in the finite plane, its bifurcations, stable manifold and lastly, the stability of the critical points in the infinite plane, afterwards the phase portraits resulting from the analysis, moreover Algebraic aspects are also included such that hamiltonian cases and Galois differential groupes. It should be noted that these families have associated oscillating type problems given their similarity to the Liénard equations.