Singular impasse points of planar constrained differential systems

• Autor(a) principal: Perez, Otavio Henrique [UNESP]
• Data de Publicação: 2022
• Outros Autores: da Silva, Paulo Ricardo [UNESP]
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://dx.doi.org/10.36045/j.bbms.220602; http://hdl.handle.net/11449/249091
• topic: blow ups; Constrained differential systems; impasses; singular perturbations; topological equivalence

Planar analytic constrained differential systems (or impasse systems) are given by (Formular Presented) where F is a vector field and A is a matrix valued function. This class of systems differs from classical ODE’s due to existence of the so called impasse set ∆ = {x : det A(x) = 0}. The dynamics near smooth impasse points is well known in the literature (see for instance [17, 28, 31]). In this paper, we use Newton polygon and weighted blow ups in order to study its phase portrait near singular points of ∆. Moreover, we apply our results in electric circuit problems.