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16 p, 737.1 KB |
Birth of limit cycles for a classe of continuous and discontinuous differential systems in (d 2)-dimension
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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 - 10.1080/14689367.2015.1102868
Dynamical Systems, Vol. 31 Núm. 3 (2016) , p. 237-250
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10 p, 300.3 KB |
Periodic solutions of Lienard differential equations via averaging theory of order two
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Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ;
Novaes, Douglas D. (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ;
Teixeira, Marco Antonio (Universidade Estadual de Campinas(Brazil). Departamento de Matemática)
For ε = 0 sufficiently small we provide sufficient conditions for the existence of periodic solutions for the Lienard differential equations of the form x + f(x)x + n2x + g(x) = ε2p1(t) + ε3p2(t), where n is a positive integer, f : R → R is a C3 function, g : R → R is a C4 function, and pi : R → R for i = 1, 2 are continuous 2π-periodic function. [...]
2015 - 10.1590/0001-3765201520140129
Anais da Academia Brasileira de Ciencias, Vol. 87 Núm. 4 (2015) , p. 1905-1913
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15 p, 424.0 KB |
Higher order averaging theory for finding periodic solutions via Brouwer degree
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Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ;
Novaes, Douglas D. (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ;
Teixeira, Marco Antonio (Universidade Estadual de Campinas(Brazil). Departamento de Matemática)
In this paper we deal with nonlinear differential systems of the form x'(t) = Xki=0εiFi(t, x) + εk+1R(t, x, ε), where Fi : R × D → Rn for i = 0, 1, · · · , k, and R : R × D × (−ε0, ε0) → Rn are continuous functions, T-periodic in the first variable, being D an open subset of Rn, and ε a small parameter. [...]
2014 - 10.1088/0951-7715/27/3/563
Nonlinearity, Vol. 27 (2014) , p. 563-583
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