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Articles, 7 records found
Articles 7 records found  
1.
22 p, 367.9 KB Lower bounds for the number of limit cycles in a generalised Rayleigh-Liénard oscillator / Euzébio, R (Federal University of Goiás. Institute of Mathematics and Statistics) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Tonon, Durval José (Federal University of Goiás. Institute of Mathematics and Statistics)
In this paper a generalised Rayleigh-Liénard oscillator is consider and lower bounds for the number of limit cycles bifurcating from weak focus equilibria and saddle connections are provided. By assuming some open conditions on the parameters of the considered system the existence of up to twelve limit cycles is provided. [...]
2022 - 10.1088/1361-6544/ac7691
Nonlinearity, Vol. 35, Issue 8 (August 2022) , p. 3883-3906  
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2.
15 p, 1.1 MB Crossing periodic orbits via first integrals / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Tonon, Durval José (Universidade Federal de Goiás. Instituto de Matemática e Estatística (Brazil)) ; Velter, Mariana Queiroz (Universidade Federal de Goiás. Instituto de Matemática e Estatística (Brazil))
We characterize the families of periodic orbits of two discontinuous piecewise differential systems in R3 separated by a plane using their first integrals. One of these discontinuous piecewise differential systems is formed by linear differential systems, and the other by nonlinear differential systems.
2020 - 10.1142/S0218127420501631
International journal of bifurcation and chaos in applied sciences and engineering, Vol. 30, Issue 11 (September 2020) , art. 2050163  
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3.
16 p, 2.3 MB Limit cycles of piecewise smooth differential equations on two dimensional torus / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Miranda Martins, Ricardo (Universidade Estadual de Campinas. Instituto de Matemática, Estatística e Computação Científica) ; Tonon, Durval José (Universidade Federal de Goiás. Instituto de Matemática e Estatística)
In this paper we study the limit cycles of some classes of piecewise smooth vector fields defined in the two dimensional torus. The piecewise smooth vector fields that we consider are composed by linear, Ricatti with constant coefficients and perturbations of these one, which are given in (3). [...]
2018 - 10.1007/s10884-017-9584-4
Journal of dynamics and differential equations, Vol. 30, Issue 3 (September 2018) , p. 1011-1027  
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4.
23 p, 764.3 KB Simultaneous occurrence of sliding and crossing limit cycles in piecewise linear planar vector fields / Cardoso, Joäo L. (Universidade Federal de Goiás. Instituto de Matemática e Estatística (Brazil)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Novaes, Douglas D. (Universidade Estadual de Campinas. Departamento de Matematica (Brazil)) ; Tonon, Durval José (Universidade Federal de Goiás. Instituto de Matemática e Estatística (Brazil))
In the present study, we consider planar piecewise linear vector fields with two zones separated by the straight line x = 0. Our goal is to study the existence of simultaneous crossing and sliding limit cycles for such a class of vector fields. [...]
2020 - 10.1080/14689367.2020.1722064
Dynamical Systems, vol. 35 3 (February 2020) p. 490-514  
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5.
20 p, 411.5 KB The symmetric periodic orbits for the two-electron atom / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Tonon, Durval José. (University of Goiás (Brasil). Institute of Mathematics and Statistics of Federal)
We analyse the existence of periodic symmetric orbits of the classical helium atom. The results obtained shows that there exists six families of periodic orbits that can be prolonged from a continuum of periodic symmetric orbits. [...]
2018 - 10.1007/s11005-018-1056-1
Letters in mathematical physics, Vol. 108, issue 8 (2018) , p. 1851-1871  
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6.
25 p, 395.7 KB Symmetric periodic orbits for the collinear charged 3-body problem / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Tonon, Durval José. (University of Goiás (Brasil). Institute of Mathematics and Statistics of Federal)
In this paper we study the existence of periodic symmetric orbits of the 3-body problem when each body possess mass and an electric charge. The main technique applied in this study is the continuation method of Poincar\'e.
2017 - 10.1063/1.4974511
Journal of Mathematical Physics, Vol. 58 (2017) , p. 22702  
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7.
10 p, 320.4 KB Limit cycles of discontinuous piecewise polynomial vector fields / de Carvalho, Tiago (Universidade Estadual Paulista (Brasil). Departamento de Matemática) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Tonon, Durval José. (University of Goiás (Brasil). Institute of Mathematics and Statistics of Federal)
When the first average function is non-zero we provide an upper bound for the maximum number of limit cycles bifurcating from the periodic solutions of the center x= -y((x^2 y^2)/2)^m and y= x((x^2 y^2)/2)^m with m 1, when we perturb it inside a class of discontinuous piecewise polynomial vector fields of degree n with k pieces. [...]
2017 - 10.1016/j.jmaa.2016.11.048
Journal of mathematical analysis and applications, Vol. 449 Núm. 1 (2017) , p. 572-579  
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