Limit cycles for discontinuous planar piecewise linear differential systems separated by one straight line and having a center [PDF]
Journal of Mathematical Analysis and Applications, 2018 From the beginning of this century more than thirty papers have been published studying the limit cycles of the discontinuous piecewise linear differential systems with two pieces separated by a straight line, but it remains open the following question ...
J. Llibre, Xiang Zhang
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On limit cycles bifurcating from the infinity in discontinuous piecewise linear differential systems [PDF]
Applied Mathematics and Computation, 2015 Agraïments: The first author is partially supported by a PROCAD-CAPES grant 88881.068 462/2014-01 and by a FAPESP grant 2013/13344-0. Agraïments: MINECO/FEDER grant UNAB13-4E-1604. The third author is partially supported by a FAPESP grant 2012/10231-7.
Márcio R. A. Gouveia +2 more
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Limit cycles of Discontinuous Piecewise Linear differential Systems [PDF]
International Journal of Bifurcation and Chaos, 2011 We study the bifurcation of limit cycles from the periodic orbits of a two-dimensional (resp. four-dimensional) linear center in ℝn perturbed inside a class of discontinuous piecewise linear differential systems.
P. T. Cardin, T. Carvalho, Jaume Llibre
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The Markus–Yamabe Conjecture Does not Hold for Discontinuous Piecewise Linear Differential Systems Separated by One Straight Line [PDF]
Journal of Dynamics and Differential Equations, 2020 The Markus-Yamabe conjecture is a conjecture on global asymptotic stability. The conjecture states that if a differentiable system x˙ = f(x) has a singularity and the Jacobian matrix Df(x) has everywhere eigenvalues with negative real part, then the singularity is a global attractor. In this paper we consider discontinuous piecewise linear differential
J. Llibre, Lucyjane de A. S. Menezes
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On the limit cycles of a class of discontinuous piecewise linear differential systems
Discrete & Continuous Dynamical Systems - B, 2020 In this paper we consider discontinuous piecewise linear differential systems whose discontinuity set is a straight line \begin{document}$ L $\end{document} which does not pass through the origin.
J. Llibre, Lucyjane de A. S. Menezes
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The Limit Cycles of Discontinuous Piecewise Linear Differential Systems Formed by Centers and Separated by Irreducible Cubic Curves II [PDF]
Differential Equations and Dynamical Systems, 2021 In this paper we provide a lower bound for the maximum number of crossing limit cycles of some class of planar discontinuous piecewise linear differential systems formed by centers and separated by an irreducible algebraic cubic curve. First we prove that the systems constituted by three zones can exhibit 0, 1, 2, 3 or 4 crossing limit cycles having ...
Rebiha Benterki +2 more
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Limit Cycles of Planar Piecewise Differential Systems with Linear Hamiltonian Saddles
Symmetry, 2021 We provide the maximum number of limit cycles for continuous and discontinuous planar piecewise differential systems formed by linear Hamiltonian saddles and separated either by one or two parallel straight lines.
J. Llibre, C. Valls
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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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The pseudo-Hopf bifurcation for planar discontinuous piecewise linear differential systems [PDF]
Nonlinear Dynamics, 2017 Agraïments: The first author wishes to thank CONACyT for the support on the PhD Scholarship Number 320218. The last author was supported by CONACyT Grant Number 180266. The creation or destruction of a crossing limit cycle when a sliding segment changes its stability, is known as pseudo-Hopf bifurcation. In this paper, under generic conditions, we find
Juan Castillo +2 more
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Limit Cycles for Discontinuous Planar Piecewise Linear Differential Systems Separated by an Algebraic Curve [PDF]
International Journal of Bifurcation and Chaos, 2019 We study how to change the maximum number of limit cycles of the discontinuous piecewise linear differential systems with only two pieces in function of the degree of the discontinuity of the algebraic curve between the two linear differential systems. These discontinuous differential systems appear frequently in applied sciences.
Jaume Llibre, Xiang Zhang
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