Results 11 to 20 of about 26,995 (188)
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
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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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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 THE DISCONTINUOUS PIECEWISE DIFFERENTIAL SYSTEMS ON THE CYLINDER
Journal of Applied Analysis & Computation, 2022 In order to understand the dynamics of the differential systems the limit cycles play a main role, but in general their study is not easy. These last years an increasing interest appeared for studying the limit cycles of some classes of discontinuous piecewise differential systems, due to the rich applications of this kind of differential systems. Very
Li, Jie, Llibre, Jaume
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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 of piecewise polynomial differential systems with the discontinuity line xy = 0
Communications on Pure & Applied Analysis, 2021 In this paper we study the maximum number of limit cycles bifurcating from the periodic orbits of the center x. = -y((x + y)/2), y. = x((x + y)/2) with m ≥ 0 under discontinuous piecewise polynomial (resp. polynomial Hamiltonian) perturbations of degree n with the discontinuity set {(x, y) ∈ R : xy = 0}. Using the averaging theory up to any order N, we
Li, Tao, Llibre, Jaume
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Centers of discontinuous piecewise smooth quasi–homogeneous polynomial differential systems
Discrete & Continuous Dynamical Systems - B, 2019 In this paper we investigate the center problem for the discontinuous piecewise smooth quasi-homogeneous but non-homogeneous polynomial differential systems. First, we provide sufficient and necessary conditions for the existence of a center in the discontinuous piecewise smooth quasi-homogeneous polynomial differential systems. Moreover, these centers
Chen, Hebai, Llibre, Jaume, Tang, Yilei
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Dynamical Systems, 2022 These last years an increasing interest appeared for studying the planar discontinuous piecewise differential systems motivated by the rich applications in modelling real phenomena. One of the difficulties for understanding the dynamics of these systems is the study their limit cycles.
Claudio A. Buzzi +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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