Global Phase Portrait and Bifurcation Diagram for a Multi-Parametric Linear System

Jorge Rodríguez Contreras, Alberto Reyes Linero, Juliana Vargas Sánchez
2020 Journal of Southwest Jiaotong University  
The goal of this article is to conduct a global dynamics study of a linear multiparameter system (real parameters (a,b,c) in R^3); for this, we take the different changes that these parameters present. First, we find the different parametric surfaces in which the space is divided, where the stability of the critical point is defined; we then create a bifurcation diagram to classify the different bifurcations that appear in the system. Finally, we determine and classify the critical points at
more » ... itical points at infinity, considering the canonical shape of the Poincaré sphere, and thus, obtain a global phase portrait of the multiparametric linear system.
doi:10.35741/issn.0258-2724.55.4.28 fatcat:n2q2q5nk2vhu7nylrqrpqbfea4