Galoisian and Qualitative Approaches to Linear Polyanin-Zaitsev Vector Fields

Acosta-Humánez, Primitivo B.; Reyes-Linero, Alberto; Rodríguez-Contreras, Jorge

doi:10.48550/arxiv.1807.05272

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Saddle-focus-saddle Bifurcations1

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2021

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“…We can find antecedents of the algebraic and qualitative studies of this family in [1,2,3,4]. Another algebraic and dynamical studies can be found in [5,6].…”

Section: Introductionmentioning

confidence: 94%

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Transcritical Bifurcations and Algebraic Aspects of Quadratic Multiparametric Families

Contreras¹,

Linero²,

Montes³

et al. 2021

Preprint

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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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“…We can find antecedents of the algebraic and qualitative studies of this family in [1,2,3,4]. Another algebraic and dynamical studies can be found in [5,6].…”

Section: Introductionmentioning

confidence: 94%

“…Algebraic Methods. Concerning algebraic aspects considered in this paper, we follow the references [16,17,18,19,20,21,22,23,24,25,26,27,28,29,30] and also [1,2,3,4,5,6].…”

Section: Saddle-focus-saddle Bifurcationsmentioning

confidence: 99%