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Birth of limit cycles for a classe of continuous and discontinuous differential systems in (d 2)-dimension / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Teixeira, Marco Antonio (Universidade Estadual de Campinas(Brazil). Departamento de Matemática) ; Zeli, Iris O. (Universidade Estadual de Campinas(Brazil). Departamento de Matemática)
The orbits of the reversible differential system ˙x = −y, ˙y = x, ˙z = 0, with x, y ∈ R and z ∈ R d, are periodic with the exception of the equilibrium points (0, 0, z1, . . . , zd). We compute the maximum number of limit cycles which bifurcate from the periodic orbits of the system ˙x = −y, ˙y = x, ˙z = 0, using the averaging theory of first order, when this system is perturbed, first inside the class of all polynomial differential systems of degree n, and second inside the class of all discontinuous piecewise polynomial differential systems of degree n with two pieces, one in y > 0 and the other in y < 0. [...]
2016 - DOI (Digital Object Identifier)

10.1080/14689367.2015.1102868
Dynamical Systems, Vol. 31 Núm. 3 (2016) , p. 237-250

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