Quadratic slow-fast systems on the plane

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.