Transcritical bifurcation in a multiparametric nonlinear system
- Resource Type
- article
- Authors
- Osmin Ferrer; José Guerra; Alberto Reyes
- Source
- AIMS Mathematics, Vol 7, Iss 8, Pp 13803-13820 (2022)
- Subject
- dynamic system
singularity
poincare compactification
stability
bifurcation
global phase portrait
Mathematics
QA1-939
- Language
- English
- ISSN
- 2473-6988
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.