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Research Article | Open Access

Transcritical bifurcation in a multiparametric nonlinear system

Osmin Ferrer1( ), José Guerra1, Alberto Reyes2
Departament of Mathematics, University of Sucre, Cra. 28 # 5-267, Puerta Roja, Sincelejo, Sucre, Colombia
Departament of Mathematics, University of Atlántico, Carrera 30 # 8-49, Puerto Colombia, Barranquilla, Atlántico, Colombia
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Abstract

In this paper we study a multiparametric nonlinear system with a transcritical bifurcation in a region of points of R 3 . The parametric regions that constitute the boundaries where important qualitative changes occur in the dynamics of the system are determined. The equilibrium points in each of the regions are also established and classified. Finally, the stability of the equilibrium points at infinity of the system obtained from the Poincare compactification is classified, and the global phase portrait of the system is made.

Keywords

dynamic systemsingularityPoincare compactificationstabilitybifurcationglobal phase portrait
CLC number: 42C15, 46C05, 46C20

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AIMS Mathematics
Volume 7 Issue 8,
August 2022
Pages 13803-13820
DOI: 10.3934/math.2022761

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Cite this article:
Ferrer O, Guerra J, Reyes A. Transcritical bifurcation in a multiparametric nonlinear system. AIMS Mathematics, 2022, 7(8): 13803-13820. https://doi.org/10.3934/math.2022761

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Received: 11 February 2022
Revised: 23 April 2022
Accepted: 26 April 2022
Published: 15 August 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)