Transcritical Bifurcations and Algebraic Aspects of Quadratic Multiparametric Families
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, st...
- Autores:
-
Rodríguez Contreras, Jorge
- Tipo de recurso:
- Fecha de publicación:
- 2021
- Institución:
- Universidad del Atlántico
- Repositorio:
- Repositorio Uniatlantico
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.uniatlantico.edu.co:20.500.12834/1143
- Acceso en línea:
- https://hdl.handle.net/20.500.12834/1143
- Palabra clave:
- Quadratic Polynomial Systems, Critical Points, Bifurcations, Stable Manifold, Phase portraits of polynomial systems.
- Rights
- openAccess
- License
- http://creativecommons.org/licenses/by-nc/4.0/
| Summary: | 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. |
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