Transcritical bifurcation in a multiparametric nonlinear system

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.

Keywords

• dynamic system
• singularity
• poincare compactification
• stability
• bifurcation
• global phase portrait