Quadratic slow-fast systems on the plane

Author(s)

Meza-Sarmiento, Ingrid S. ^[1] ; Oliveira, Regilene ^[2] ; Silva, Paulo R. da ^[3]

Affiliation

^[1] Univ Fed Sao Carlos, Dept Matemat, Rod Washington Luis Km 235, SP 310, BR-13565905 Sao Carlos, SP - Brazil

^[2] Univ Sao Paulo, ICMC, Dept Matemat, Ave Trabalhador Sao Carlense 400, BR-13566590 Sao Carlos, SP - Brazil

^[3] UNESP, IBILCE, Dept Matemat, Rua C Colombo 2265, BR-15054000 Sao Jose Do Rio Preto, SP - Brazil

• Document type: Journal article
• Source: NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS; v. 60, AUG 2021.
• Web of Science Citations: 1

Abstract

In this paper singularly perturbed quadratic polynomial differential systems e(x) over dot = P-epsilon(x, y) = P(x, y, epsilon), (y) over dot = Q(epsilon)(x, y) = Q(x, y, epsilon) with x, y is an element of R, epsilon >= 0 and (P-epsilon, Q(epsilon)) = 1 for epsilon > 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 Poincare disc when epsilon = 0. For epsilon > 0, we present the possible local behavior of the solutions near of a finite and infinite equilibrium point under suitable conditions. More specifically, if p(0) is a finite equilibrium point then we obtain the local behavior for epsilon > 0 using Fenichel theory. Assuming that p(0) is an infinite equilibrium point, there exists K subset of M-0 normally hyperbolic and p(0) is an element of M-0' boolean AND K using the Poincare compactification and algebraic invariant we describe globally the dynamics for epsilon > 0 small of some classes of equivalence. (C) 2021 Elsevier Ltd. All rights reserved. (AU)

• FAPESP's process: 19/21181-0 - New frontiers in Singularity Theory
• Grantee: Regilene Delazari dos Santos Oliveira
• Support Opportunities: Research Projects - Thematic Grants