Transcritical bifurcation in a multiparametric nonlinear system

Osmin Ferrer; José Guerra; Alberto Reyes; Osmin Ferrer; José Guerra; Alberto Reyes

doi:10.3934/math.2022761

AIMS Mathematics

2022, Volume 7, Issue 8: 13803-13820. doi: 10.3934/math.2022761

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Research article

Transcritical bifurcation in a multiparametric nonlinear system

1.
Departament of Mathematics, University of Sucre, Cra. 28 # 5-267, Puerta Roja, Sincelejo, Sucre, Colombia
2.
Departament of Mathematics, University of Atlántico, Carrera 30 # 8-49, Puerto Colombia, Barranquilla, Atlántico, Colombia

Received: 11 February 2022 Revised: 23 April 2022 Accepted: 26 April 2022 Published: 23 May 2022
MSC : 42C15, 46C05, 46C20

In this paper we study a multiparametric nonlinear system with a transcritical bifurcation in a region of points of $ \mathbb{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.
- dynamic system,
- singularity,
- Poincare compactification,
- stability,
- bifurcation,
- global phase portrait
Citation: Osmin Ferrer, José Guerra, Alberto Reyes. Transcritical bifurcation in a multiparametric nonlinear system[J]. AIMS Mathematics, 2022, 7(8): 13803-13820. doi: 10.3934/math.2022761

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Abstract

In this paper we study a multiparametric nonlinear system with a transcritical bifurcation in a region of points of $ \mathbb{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.

References

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