| Full text | |
| Author(s): |
Total Authors: 3
|
| Affiliation: | [1] Univ Estadual Paulista, Dept Matemat, Sao Jose Do Rio Preto - Brazil
[2] Univ Fed ABC, Ctr Matemat Comp & Cognicao, BR-09210170 Santo Andre, SP - Brazil
[3] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona - Spain
Total Affiliations: 3
|
| Document type: | Journal article |
| Source: | PHYSICA D-NONLINEAR PHENOMENA; v. 371, p. 28-47, MAY 15 2018. |
| Web of Science Citations: | 0 |
| Abstract | |
A classical perturbation problem is the polynomial perturbation of the harmonic oscillator, (x', y') = (-y + epsilon f(x, y, epsilon), x + epsilon g(x, y, epsilon)). In this paper we study the limit cycles that bifurcate from the period annulus via piecewise polynomial perturbations in two zones separated by a straight line. We prove that, for polynomial perturbations of degree n, no more than Nn-1 limit cycles appear up to a study of order N. We also show that this upper bound is reached for orders one and two. Moreover, we study this problem in some classes of piecewise Lienard differential systems providing better upper bounds for higher order perturbation in 8, showing also when they are reached. The Poincare-Pontryagin-Melnikov theory is the main technique used to prove all the results. (C) 2018 Elsevier B.V. All rights reserved. (AU) | |
| FAPESP's process: | 17/03352-6 - Limit cycles in some piecewise differential systems |
| Grantee: | Claudio Aguinaldo Buzzi |
| Support Opportunities: | Research Grants - Visiting Researcher Grant - International |
| FAPESP's process: | 12/18780-0 - Geometry of control systems, dynamical and stochastics systems |
| Grantee: | Marco Antônio Teixeira |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 13/24541-0 - Ergodic and qualitative theory of dynamical systems |
| Grantee: | Claudio Aguinaldo Buzzi |
| Support Opportunities: | Research Projects - Thematic Grants |