Quadratic slow-fast systems on the plane

Nenhuma Miniatura disponível

Data

2021-08-01

Autores

Meza-Sarmiento, Ingrid S.
Oliveira, Regilene
da Silva, Paulo R. [UNESP]

Título da Revista

ISSN da Revista

Título de Volume

Editor

Resumo

In this paper singularly perturbed quadratic polynomial differential systems εẋ=Pε(x,y)=P(x,y,ε),ẏ=Qε(x,y)=Q(x,y,ε)with x,y∈R,ε⩾0 and (Pε,Qε)=1 for ε>0, are considered. We prove that there are 10 classes of equivalence for these systems. We describe the dynamics of these 10 classes on the Poincaré disc when ε=0. For ε>0, we present the possible local behavior of the solutions near of a finite and infinite equilibrium point under suitable conditions. More specifically, if p0 is a finite equilibrium point then we obtain the local behavior for ε>0 using Fenichel theory. Assuming that p0 is an infinite equilibrium point, there exists K⊂M0 normally hyperbolic and p0∈M0′∩K using the Poincaré compactification and algebraic invariant we describe globally the dynamics for ε>0 small of some classes of equivalence.

Descrição

Palavras-chave

Quadratic system, Singular perturbation, Topological invariant, Vector field

Como citar

Nonlinear Analysis: Real World Applications, v. 60.