On cyclicity in discontinuous piecewise linear near-Hamiltonian differential systems with three zones having a saddle in the central one

被引：3

作者：

Pessoa, Claudio ^{[1
]}

Ribeiro, Ronisio ^{[4
]}

Novaes, Douglas ^{[2
]}

Gouveia, Marcio ^{[1
]}

Euzebio, Rodrigo ^{[3
]}

机构：

[1] Univ Estadual Paulista UNESP, Inst Biociencias Letras & Ciencias Exatas, R Cristovao Colombo 2265, BR-15054000 Sao Jose Do Rio Preto, SP, Brazil

[2] Univ Estadual Campinas UNICAMP, Dept Matemat, R Sergio Buarque de Holanda 651, BR-13083859 Campinas, SP, Brazil

[3] Univ Fed Goias UFG, Inst Matemat & Estat, BR-74690900 Goiania, Go, Brazil

[4] Univ Fed Itajuba UNIFEI, Inst Matemat & Comp, Ave BPS 1303, BR-37500903 Itajuba, MG, Brazil

来源：

NONLINEAR DYNAMICS | 2023年 / 111卷 / 22期

基金：

瑞典研究理事会; 巴西圣保罗研究基金会;

关键词：

Limit cycle; Piecewise Hamiltonian differential system; Melnikov function; Periodic annulus; LIMIT-CYCLES; PLANAR SYSTEMS; BIFURCATION; NUMBER;

D O I：

10.1007/s11071-023-08931-8

中图分类号：

TH [机械、仪表工业];

学科分类号：

0802 ;

摘要：

We obtain lower bounds for the maximum number of limit cycles bifurcating from periodic annuli of discontinuous planar piecewise linear Hamiltonian differential systems with three zones separated by two parallel straight lines, assuming that the linear differential subsystem in the region between the two straight lines, called of central subsystem, has a saddle at a point equidistant from these lines. (Obviously, the other subsystems have saddles or centers.) We prove that at least six limit cycles bifurcate from the periodic annuli of these kind of piecewise Hamiltonian differential systems, by linear perturbations. Normal forms and Melnikov functions, defined in two and three zones, are the main techniques used in the proof of the results.

引用

页码：21153 / 21175

页数：23