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AxiomsIn this article, we study the maximum number of limit cycles of discontinuous piecewise differential systems, formed by two Hamiltonians systems separated by a straight line.
Joyce A. Casimiro, Jaume Llibre
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On the limit cycles for a class of discontinuous piecewise cubic polynomial differential systems
Electronic Journal of Qualitative Theory of Differential Equations, 2020 This paper presents new results on the bifurcation of medium and small limit cycles from the periodic orbits surrounding a cubic center or from the cubic center that have a rational first integral of degree 2 respectively, when they are perturbed inside ...
Bo Huang
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Averaging theory for discontinuous piecewise differential systems [PDF]
Journal of Differential Equations, 2021 Agraïments: The first author is partially supported by FEDER-UNAB10-4E-378. The second author is partially supported by a FAPESP-BRAZIL grant 2012/18780-0 and a CNPq grant 449655/2014-8. The third author is partially supported by a FAPESP-BRAZIL grant 2012/10231-7.
Jaume Llibre +2 more
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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
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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. Our main result shows that at most 1 (resp.
Cardin, Pedro Toniol +2 more
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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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Limit Cycles of Polynomially Integrable Piecewise Differential Systems
Axioms, 2023 In this paper, we study how many algebraic limit cycles have the discontinuous piecewise linear differential systems separated by a straight line, with polynomial first integrals on both sides.
Belén García +3 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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Electronic Journal of Qualitative Theory of Differential Equations, 2021 Due to their applications to many physical phenomena during these last decades the interest for studying the discontinuous piecewise differential systems has increased strongly.
Rebiha Benterki +2 more
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Characterisation of Singular Domains in Threshold-Dependent Biological Networks
Journal of Nigerian Society of Physical Sciences, 2022 Threshold-dependent networks behave like piecewise smooth system which belongs to a class of systems with discontinuous right hand side. It can be studied with piecewise linear differential equations.
Benitho Ngwu +5 more
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