2015
9.
Jaume Llibre; Douglas D. Novaes; Marco A. Teixeira
Periodic solutions of Lienard differential equations via averaging theory of order two Journal Article
Em: Anais da Academia Brasileira de Ciências, vol. 87, não 4, pp. 1905-1913, 2015.
@article{LliNovTeiABC2015,
title = {Periodic solutions of Lienard differential equations via averaging theory of order two},
author = {Jaume Llibre and Douglas D. Novaes and Marco A. Teixeira},
url = {http://dx.doi.org/10.1590/0001-3765201520140129},
doi = {10.1590/0001-3765201520140129},
year = {2015},
date = {2015-01-01},
journal = {Anais da Academia Brasileira de Ciências},
volume = {87},
number = {4},
pages = {1905-1913},
publisher = {FapUNIFESP (SciELO)},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
8.
Jaume Llibre; Douglas D. Novaes; Marco A. Teixeira
Limit Cycles Bifurcating from the Periodic Orbits of a Discontinuous Piecewise Linear Differentiable Center with Two Zones Journal Article
Em: International Journal of Bifurcation and Chaos, vol. 25, não 11, pp. 1550144, 2015.
@article{LliNovTeiJBC2015,
title = {Limit Cycles Bifurcating from the Periodic Orbits of a Discontinuous Piecewise Linear Differentiable Center with Two Zones},
author = {Jaume Llibre and Douglas D. Novaes and Marco A. Teixeira},
url = {http://dx.doi.org/10.1142/S0218127415501448},
doi = {10.1142/S0218127415501448},
year = {2015},
date = {2015-01-01},
journal = {International Journal of Bifurcation and Chaos},
volume = {25},
number = {11},
pages = {1550144},
abstract = {We study a class of discontinuous piecewise linear differential systems with two zones separated by the straight line x = 0. In x > 0, we have a linear saddle with its equilibrium point living in x > 0, and in x < 0 we have a linear differential center. Let p be the equilibrium point of this linear center, when p lives in x < 0, we say that it is real, and when p lives in x > 0 we say that it is virtual. We assume that this discontinuous piecewise linear differential system formed by the center and the saddle has a center q surrounded by periodic orbits ending in a homoclinic orbit of the saddle, independent if p is real, virtual or p is in x = 0. Note that q = p if p is real or p is in x = 0. We perturb these three classes of systems, according to the position of p, inside the class of all discontinuous piecewise linear differential systems with two zones separated by x = 0. Let N be the maximum number of limit cycles which can bifurcate from the periodic solutions of the center q with these perturbations. Our main results show that N = 2 when p is on x = 0, and N ≥ 2 when p is a real or virtual center. Furthermore, when p is a real center we found an example satisfying N ≥ 3.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We study a class of discontinuous piecewise linear differential systems with two zones separated by the straight line x = 0. In x > 0, we have a linear saddle with its equilibrium point living in x > 0, and in x < 0 we have a linear differential center. Let p be the equilibrium point of this linear center, when p lives in x < 0, we say that it is real, and when p lives in x > 0 we say that it is virtual. We assume that this discontinuous piecewise linear differential system formed by the center and the saddle has a center q surrounded by periodic orbits ending in a homoclinic orbit of the saddle, independent if p is real, virtual or p is in x = 0. Note that q = p if p is real or p is in x = 0. We perturb these three classes of systems, according to the position of p, inside the class of all discontinuous piecewise linear differential systems with two zones separated by x = 0. Let N be the maximum number of limit cycles which can bifurcate from the periodic solutions of the center q with these perturbations. Our main results show that N = 2 when p is on x = 0, and N ≥ 2 when p is a real or virtual center. Furthermore, when p is a real center we found an example satisfying N ≥ 3.
7.
Márcio R. A. Gouveia; Jaume Llibre; Douglas D. Novaes
On limit cycles bifurcating from the infinity in discontinuous piecewise linear differential systems Journal Article
Em: Applied Mathematics and Computation, vol. 271, pp. 365 - 374, 2015.
@article{GouLliNovAPC2015,
title = {On limit cycles bifurcating from the infinity in discontinuous piecewise linear differential systems},
author = {Márcio R. A. Gouveia and Jaume Llibre and Douglas D. Novaes},
url = {http://dx.doi.org/10.1016/j.amc.2015.09.022},
doi = {10.1016/j.amc.2015.09.022},
year = {2015},
date = {2015-01-01},
journal = {Applied Mathematics and Computation},
volume = {271},
pages = {365 - 374},
abstract = {Abstract In this paper we consider the linear differential center (x',y') = (− y , x ) perturbed inside the class of all discontinuous piecewise linear differential systems with two zones separated by the straight line y = 0 . Using the Bendixson transformation we provide sufficient conditions to ensure the existence of a crossing limit cycle coming purely from the infinity. We also study the displacement function for a class of discontinuous piecewise smooth differential system.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Abstract In this paper we consider the linear differential center (x',y') = (− y , x ) perturbed inside the class of all discontinuous piecewise linear differential systems with two zones separated by the straight line y = 0 . Using the Bendixson transformation we provide sufficient conditions to ensure the existence of a crossing limit cycle coming purely from the infinity. We also study the displacement function for a class of discontinuous piecewise smooth differential system.
6.
Douglas D. Novaes; Mike R. Jeffrey
Regularization of hidden dynamics in piecewise smooth flows Journal Article
Em: Journal of Differential Equations, vol. 259, não 9, pp. 4615 - 4633, 2015.
@article{NovJefJDE2015,
title = {Regularization of hidden dynamics in piecewise smooth flows},
author = {Douglas D. Novaes and Mike R. Jeffrey},
url = {http://dx.doi.org/10.1016/j.jde.2015.06.005},
doi = {10.1016/j.jde.2015.06.005},
year = {2015},
date = {2015-01-01},
journal = {Journal of Differential Equations},
volume = {259},
number = {9},
pages = {4615 - 4633},
abstract = {This paper studies the equivalence between differentiable and non-differentiable dynamics in Rn . Filippov's theory of discontinuous differential equations allows us to find flow solutions of dynamical systems whose vector fields undergo switches at thresholds in phase space. The canonical convex combination at the discontinuity is only the linear part of a nonlinear combination that more fully explores Filippov's most general problem: the differential inclusion. Here we show how recent work relating discontinuous systems to singular limits of continuous (or regularized) systems extends to nonlinear combinations. We show that if sliding occurs in a discontinuous systems, there exists a differentiable slow–fast system with equivalent slow invariant dynamics. We also show the corresponding result for the pinching method, a converse to regularization which approximates a smooth system by a discontinuous one.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
This paper studies the equivalence between differentiable and non-differentiable dynamics in Rn . Filippov's theory of discontinuous differential equations allows us to find flow solutions of dynamical systems whose vector fields undergo switches at thresholds in phase space. The canonical convex combination at the discontinuity is only the linear part of a nonlinear combination that more fully explores Filippov's most general problem: the differential inclusion. Here we show how recent work relating discontinuous systems to singular limits of continuous (or regularized) systems extends to nonlinear combinations. We show that if sliding occurs in a discontinuous systems, there exists a differentiable slow–fast system with equivalent slow invariant dynamics. We also show the corresponding result for the pinching method, a converse to regularization which approximates a smooth system by a discontinuous one.
2014
5.
Jaume Llibre; Douglas D. Novaes; Marco A. Teixeira
Higher order averaging theory for finding periodic solutions via Brouwer degree Journal Article
Em: Nonlinearity, vol. 27, não 3, pp. 563, 2014.
@article{LliNovTeiN2014,
title = {Higher order averaging theory for finding periodic solutions via Brouwer degree},
author = {Jaume Llibre and Douglas D. Novaes and Marco A. Teixeira},
url = {http://dx.doi.org/10.1088/0951-7715/27/3/563},
doi = {10.1088/0951-7715/27/3/563},
year = {2014},
date = {2014-01-01},
journal = {Nonlinearity},
volume = {27},
number = {3},
pages = {563},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
4.
Jaume Llibre; Douglas D. Novaes; Marco A. Teixeira
Corrigendum: Higher order averaging theory for finding periodic solutions via Brouwer degree (2014 Nonlinearity 27 563) Journal Article
Em: Nonlinearity, vol. 27, não 9, pp. 2417, 2014.
@article{LliNovTeiN2014c,
title = {Corrigendum: Higher order averaging theory for finding periodic solutions via Brouwer degree (2014 Nonlinearity 27 563)},
author = {Jaume Llibre and Douglas D. Novaes and Marco A. Teixeira},
url = {http://dx.doi.org/10.1088/0951-7715/27/9/2417},
doi = {10.1088/0951-7715/27/9/2417},
year = {2014},
date = {2014-01-01},
journal = {Nonlinearity},
volume = {27},
number = {9},
pages = {2417},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
3.
Douglas D. Novaes
On nonsmooth perturbations of nondegenerate planar centers Journal Article
Em: Publicacions Matemàtiques, vol. EXTRA, pp. 395-420, 2014.
@article{NovPM2014,
title = {On nonsmooth perturbations of nondegenerate planar centers},
author = {Douglas D. Novaes},
url = {http://dx.doi.org/10.5565/publmat_extra14_20},
doi = {10.5565/publmat_extra14_20},
year = {2014},
date = {2014-01-01},
urldate = {2014-01-01},
journal = {Publicacions Matemàtiques},
volume = {EXTRA},
pages = {395-420},
publisher = {Universitat Autonoma de Barcelona},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
2013
2.
Douglas D. Novaes
Perturbed damped pendulum: finding periodic solutions via averaging method Journal Article
Em: Revista Brasileira de Ensino de Física, vol. 35, não 1, pp. 01-07, 2013.
@article{NovaesRBEF2013,
title = {Perturbed damped pendulum: finding periodic solutions via averaging method},
author = {Douglas D. Novaes},
url = {http://dx.doi.org/10.1590/s1806-11172013000100014},
doi = {10.1590/s1806-11172013000100014},
year = {2013},
date = {2013-01-01},
journal = {Revista Brasileira de Ensino de Física},
volume = {35},
number = {1},
pages = {01-07},
publisher = {FapUNIFESP (SciELO)},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
2011
1.
Jaume Llibre; Douglas D. Novaes; Marco A. Teixeira
On the periodic solutions of a perturbed double pendulum Journal Article
Em: The São Paulo Journal of Mathematical Sciences, vol. 5, não 2, pp. 317, 2011.
@article{LliNovTeiSPJMS2011,
title = {On the periodic solutions of a perturbed double pendulum},
author = {Jaume Llibre and Douglas D. Novaes and Marco A. Teixeira},
url = {http://dx.doi.org/10.11606/issn.2316-9028.v5i2p317-330},
doi = {10.11606/issn.2316-9028.v5i2p317-330},
year = {2011},
date = {2011-01-01},
journal = {The São Paulo Journal of Mathematical Sciences},
volume = {5},
number = {2},
pages = {317},
publisher = {Universidade de Sao Paulo Sistema Integrado de Bibliotecas - SIBiUSP},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
