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On the periodic solutions of the Michelson continuous and discontinuous piecewise linear differential system [PDF]
Computational and Applied Mathematics, 2018 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.
J. Llibre +2 more
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International Journal of Bifurcation and Chaos
In this paper, we investigate the existence of limit cycles in piecewise linear systems separated by two parallel straight lines, where in one of these straight lines, the piecewise differential system is continuous, and in the other, it is discontinuous.
A. Berbache
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In this paper, we investigate the existence of limit cycles in piecewise linear systems separated by two parallel straight lines, where in one of these straight lines, the piecewise differential system is continuous, and in the other, it is discontinuous.
A. Berbache
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Nonlinear Dynamics, 2013
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de Carvalho Braga, Denis +1 more
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
de Carvalho Braga, Denis +1 more
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Qualitative Theory of Dynamical Systems, 2022
Discontinuous planar piecewise linear differential system of the focus-center type and the center-center type with a straight line of separation are being studied. The global topological classification of these systems on the Poincaré disc is studied. 60 phase portraits on the Poincaré disc up to topological equivalence are obtained.
Lizhong Xiong, Kuilin Wu, Shimin Li
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Discontinuous planar piecewise linear differential system of the focus-center type and the center-center type with a straight line of separation are being studied. The global topological classification of these systems on the Poincaré disc is studied. 60 phase portraits on the Poincaré disc up to topological equivalence are obtained.
Lizhong Xiong, Kuilin Wu, Shimin Li
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São Paulo Journal of Mathematical Sciences, 2022 The authors investigate the existence of periodic solutions for a planar discontinuous system of differential equations, which is a perturbation of a piecewise linear Hamiltonian system possessing either a homoclinic loop or a heteroclinic orbit. It is assumed that the Hamiltonian system has a center in the central strip and saddle points in the other ...
Claudio Pessoa, R. Ribeiro
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Nonlinear Analysis: Real World Applications, 2022
In this paper, we study the number of limit cycles that can bifurcate from a periodic annulus in discontinuous planar piecewise linear Hamiltonian differential system with three zones separated by two parallel straight lines, such that the linear ...
Claudio Pessoa, R. Ribeiro
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In this paper, we study the number of limit cycles that can bifurcate from a periodic annulus in discontinuous planar piecewise linear Hamiltonian differential system with three zones separated by two parallel straight lines, such that the linear ...
Claudio Pessoa, R. Ribeiro
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Differential Equations and Dynamical Systems
Meriem Barkat, Rebiha Benterki
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Meriem Barkat, Rebiha Benterki
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Nonlinearity, 2023
In this paper periodic trajectories of dynamical systems presenting discontinuities are studied. The considered model consists of two distinct linear differential systems, each one containing a single equilibrium point of centre type.
Á. Alves, R. Euzébio
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In this paper periodic trajectories of dynamical systems presenting discontinuities are studied. The considered model consists of two distinct linear differential systems, each one containing a single equilibrium point of centre type.
Á. Alves, R. Euzébio
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International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 2023
The main topic studied in this article is the number of crossing limit cycles bifurcating from two or three period annuli in discontinuous planar piecewise linear Hamiltonian differential systems with three zones.
Denis de Carvalho Braga +4 more
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The main topic studied in this article is the number of crossing limit cycles bifurcating from two or three period annuli in discontinuous planar piecewise linear Hamiltonian differential systems with three zones.
Denis de Carvalho Braga +4 more
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Planar systems of piecewise linear differential equations with a line of discontinuity
Nonlinearity, 2001The authors study dynamical properties of the planar system \[ \dot u= Au+sgn( w^{T}u) v, \] where \(A\) is a real \(2\times 2\)-matrix and \(u, v, w\) are two-dimensional real vectors. The dependence on the system parameters \(A,v\) and \(w,\) including the existence of periodic solutions with sliding motion, is analyzed.
Giannakopoulos, Fotios, Pliete, Karin
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