On limit cycles bifurcating from the infinity in discontinuous piecewise linear differential systems

Author(s)

Gouveia, Marcio R. A. ^[1] ; Llibre, Jaume ^[2] ; Novaes, Douglas D. ^[3]

Affiliation

^[1] Univ Estadual Paulista, IBILCE, Dept Matemat, BR-15054000 Sao Paulo - Brazil

^[2] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Catalonia - Spain

^[3] Univ Estadual Campinas, Dept Matemat, BR-13083859 Campinas, SP - Brazil

• Document type: Journal article
• Source: Applied Mathematics and Computation; v. 271, p. 365-374, NOV 15 2015.
• Web of Science Citations: 3

Abstract

In this paper we consider the linear differential center ((x) over dot, (y) over dot) = (-y, x) perturbed inside the class of all discontinuous piecewise linear differential systems with two zones separated by the straight line y = 0. Using the Bendixson transformation we provide sufficient conditions to ensure the existence of a crossing limit cycle coining purely from the infinity. We also study the displacement function for a class of discontinuous piecewise smooth differential system. (C) 2015 Elsevier Inc. All rights reserved. (AU)

• FAPESP's process: 12/10231-7 - Regularization and minimal sets for non-smooth dynamical systems
• Grantee: Douglas Duarte Novaes
• Support type: Scholarships in Brazil - Doctorate
• FAPESP's process: 13/13344-0 - Existence of periodic orbits using Lefschetz and Nielsen numbers theory
• Grantee: Márcio Ricardo Alves Gouveia
• Support type: Scholarships abroad - Research