Open AccessGlobal Phase Portrait and Bifurcation Diagram for a Multi-Parametric Linear System
Author(s) -
Jorge Rodríguez Contreras,
Alberto Reyes Linero,
Juliana Vargas Sánchez
Publication year - 2020
Publication title -
xi'nan jiaotong daxue xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.308
H-Index - 21
ISSN - 0258-2724
DOI - 10.35741/issn.0258-2724.55.4.28
Subject(s) - phase portrait , bifurcation diagram , bifurcation , parametric statistics , phase diagram , parameter space , stability (learning theory) , mathematics , point (geometry) , phase space , diagram , infinity , space (punctuation) , statistical physics , mathematical analysis , nonlinear system , phase (matter) , physics , computer science , geometry , statistics , quantum mechanics , machine learning , thermodynamics , operating system
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 infinity, considering the canonical shape of the Poincaré sphere, and thus, obtain a global phase portrait of the multiparametric linear system.