Transcritical Bifurcations and Algebraic Aspects of Quadratic Multiparametric Families
| Autor: | Primitivo B. Acosta Humánez, Jorge Rodríguez Contreras, Alberto Reyes Linero, Bladimir Blanco Montes |
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| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Phase portrait Plane (geometry) General Mathematics 010102 general mathematics Dynamical Systems (math.DS) 01 natural sciences Stability (probability) Stable manifold 010101 applied mathematics Quadratic equation Mathematics - Classical Analysis and ODEs Classical Analysis and ODEs (math.CA) FOS: Mathematics 0101 mathematics Algebraic number Mathematics - Dynamical Systems Hamiltonian (control theory) Differential (mathematics) Mathematics |
| Popis: | 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 of these families are graphed. To properly perform this study it was necessary to use some results of the non-linear systems theory, for this reason vital definitions and theorems were included because of their importance during the study of the multiparametric families. Algebraic aspects are also included. 28 pages, 12 figures |
| Databáze: | OpenAIRE |
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