Periodic orbits of continuous and discontinuous piecewise linear differential systems via first integrals [PDF]
São Paulo Journal of Mathematical Sciences, 2017 Agraïments: The first author is partially supported by FEDER-UNAB-10-4E-378 and a CAPES grant 88881.
Llibre, Jaume, Teixeira, Marco Antonio
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Phase Portraits of a Class of Continuous Piecewise Linear Differential Systems. [PDF]
Differ Equ Dyn Syst, 2023 Abstract The phase portraits of the planar linear differential systems are very well known. This is not the case for the phase portraits of the planar continuous piecewise linear differential systems. In this paper we classify the phase portraits of the class of planar continuous piecewise linear differential systems of the form
Li J, Llibre J.
europepmc +5 more sources
On the periodic solutions of the Michelson continuous and discontinuous piecewise linear differential system [PDF]
Computational and Applied Mathematics, 2016 Applying new results from the averaging theory for continuous and discontinuous differential systems, we study the periodic solutions of two distinct versions of the Michel- son differential system: a Michelson continuous piecewise linear differential system and a Michelson discontinuous piecewise linear differential system.
Llibre, Jaume +2 more
exaly +8 more sources
Phase portraits of continuous piecewise linear Liénard differential systems with three zones [PDF]
Chaos, Solitons & Fractals, 2021 Phase portraits are an invaluable tool in studying differential systems. Most of known results about global phase portraits are related to the smooth differential systems. This paper deals with a class of planar continuous piecewise linear Liénard differential systems with three zones separated by two vertical lines without symmetry.
Li, Shimin, Llibre, Jaume
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On limit cycles of piecewise differential systems formed by arbitrary linear systems and a class of quadratic systems [PDF]
Mathematica Bohemica, 2023 We study the continuous and discontinuous planar piecewise differential systems separated by a straight line and formed by an arbitrary linear system and a class of quadratic center.
Aziza Berbache
doaj +1 more source
The Markus–Yamabe conjecture for continuous and discontinuous piecewise linear differential systems [PDF]
Proceedings of the American Mathematical Society, 2021 In 1960 Markus and Yamabe made the following conjecture: If a C 1 C^1 differential system x ˙ = F ( x ) \dot {\mathbf {x}}=F(\mathbf {x}) in R
Llibre, Jaume, Zhang, Xiang
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LIMIT CYCLES FOR A CLASS OF CONTINUOUS PIECEWISE LINEAR DIFFERENTIAL SYSTEMS WITH THREE ZONES [PDF]
International Journal of Bifurcation and Chaos, 2012 In this paper, we consider a class of planar continuous piecewise linear vector fields with three zones. Using the Poincaré map, we show that these systems admit always a unique limit cycle, which is hyperbolic.
Lima, Mauricio Firmino Silva +1 more
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Reversible periodic orbits in a class of 3D continuous piecewise linear systems of differential equations [PDF]
Nonlinear Analysis: Theory, Methods & Applications, 2021 Agraïments: This work was partially supported by the Consejería de Educación y Ciencia de la Junta de Andalucía (TIC-0130, P08-FQM-03770). The second author is supported by Ministerio de Educaci'on, grant AP2008-02486.
Carmona, Victoriano +4 more
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Limit cycles of planar piecewise linear Hamiltonian differential systems with two or three zones
Electronic Journal of Qualitative Theory of Differential Equations, 2022 In this paper, we study the existence of limit cycles in continuous and discontinuous planar piecewise linear Hamiltonian differential system with two or three zones separated by straight lines and such that the linear systems that define the piecewise ...
Claudio Pessoa, Ronisio Ribeiro
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Phase portraits of piecewise linear continuous differential systems with two zones separated by a straight line [PDF]
Journal of Differential Equations, 2021 This paper provides the classification of the phase portraits in the Poincaré disc of all piecewise linear continuous differential systems with two zones separated by a straight line having a unique finite singular point which is a node or a focus. The sufficient and necessary conditions for existence and uniqueness of limit cycles are also given.
Shimin Li, Jaume Llibre
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