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Artículos, Encontrados 14 registros
Artículos Encontrados 14 registros  1 - 10siguiente  ir al registro:
1.
The limit cycles of a class of piecewise differential systems / Benabdallah, Imane (University Mohamed El Bachir. Department of Mathematics) ; Benterki, Rebiha (University Mohamed El Bachir. Department of Mathematics) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this century many papers have been published on the piecewise differential systems in the plane. The increasing interest for this class of differential systems is motivated by their many applications for modelling several natural phenomena. [...]
2023 - 10.1007/s40590-023-00535-x
Boletin de la Sociedad Matematica Mexicana, Vol. 29, Issue 3 (November 2023) , art. 62  
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2.
13 p, 959.5 KB Symmetric Phase Portraits of Homogeneous Polynomial Hamiltonian Systems of Degree 1, 2, 3, 4, and 5 with Finitely Many Equilibria / Benterki, Rebiha (University Mohamed El Bachir El Ibrahimi. Department of Mathematics) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Roughly speaking, the Poincaré disc D2 is the closed disc centered at the origin of the coordinates of R2, where the whole of R2 is identified with the interior of D2 and the circle of the boundary of D2 is identified with the infinity of R2, because in the plane R2, we can go to infinity in as many directions as points have the circle. [...]
2023 - 10.3390/sym15081476
Symmetry, Vol. 15, Issue 8 (August 2023) , art. 1476  
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3.
15 p, 350.7 KB The extended 16th Hilbert problem for a class of discontinuous piecewise differential systems / Barkat, Meriem (University Mohamed El Bachir El Ibrahimi of Bordj Bou Arréridj. Department of Mathematics) ; Benterki, Rebiha (University Mohamed El Bachir El Ibrahimi of Bordj Bou Arréridj. Department of Mathematics) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In order to understand the dynamics of the planar 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 piecewise differential systems, due to the rich applications of this kind of differential systems. [...]
2023 - 10.1007/s11071-022-07891-9
Nonlinear Dynamics, Vol. 111, Issue 2 (January 2023) , p. 1475-1484  
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4.
38 p, 2.1 MB Limit cycles of planar discontinuous piecewise linear hamiltonian systems without equilibria separated by reducible cubics / Benterki, Rebiha (Université Mohamed El Bachir El Ibrahimi. Département de Mathématiques (Algeria)) ; Jimenez Ruiz, Jeidy Johana (Universidade Federal do Oeste da Bahia (Brazil)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Due to their applications to many physical phenomena during these last decades the interest for studying the discontinuous piecewise differential systems has increased strongly. The limit cycles play a main role in the study of any planar differential system, but to determine the maximum number of limits cycles that a class of planar differential systems can have is one of the main problems in the qualitative theory of the planar differential systems. [...]
2021 - 10.14232/ejqtde.2021.1.69
Electronic Journal of Qualitative Theory of Differential Equations, Vol. 2021, Issue 69 (2021) , p. 1-38
2 documentos
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5.
25 p, 1.2 MB The limit cycles of discontinuous piecewise linear differential systems formed by centers and separated by irreducible cubic curves II / Benterki, Rebiha (Université Mohamed El Bachir El Ibrahimi. Département de Mathématiques (Algeria)) ; Damene, Loubna (Université Mohamed El Bachir El Ibrahimi. Département de Mathématiques (Algeria)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
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. [...]
2021 - 10.1007/s12591-021-00564-w
Differential Equations and Dynamical Systems, (February 2021)  
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6.
17 p, 674.0 KB The solution of the second part of the 16th Hilbert problem for nine families of discontinuous piecewise differential systems / Benterki, Rebiha (Université Mohamed El Bachir El Ibrahimi. Département de Mathématiques (Algeria)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We provide the maximum number of limit cycles of some classes of discontinuous piecewise differential systems formed by two differential systems separated by a straight line, when these differential systems are linear centers or three families of cubic isochronous centers, giving rise to ten different classes of discontinuous piecewise differential systems. [...]
2020 - 10.1007/s11071-020-06045-z
Nonlinear Dynamics, Vol. 102, Issue 4 (December 2020) , p. 2453-2466  
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7.
14 p, 596.0 KB Crossing limit cycles of planar piecewise linear Hamiltonian systems without equilibrium points / Benterki, Rebiha (Université Mohamed El Bachir El Ibrahimi. Département de Mathématiques (Algeria)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper, we study the existence of limit cycles of planar piecewise linear Hamiltonian systems without equilibrium points. Firstly, we prove that if these systems are separated by a parabola, they can have at most two crossing limit cycles, and if they are separated by a hyperbola or an ellipse, they can have at most three crossing limit cycles. [...]
2020 - 10.3390/MATH8050755
Mathematics, Vol. 8, Issue 5 (May 2020) , art. 755
2 documentos
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8.
11 p, 295.2 KB Periodic solutions of a class of Duffing differential equations / Benterki, Rebiha (Université de Bordj Bou Arréridj. Département de Mathématiques (Algeria)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this work we study the existence of new periodic solutions for the well knwon class of Duffing differential equation of the form x" + cx' + a(t)x + b(t)x3 = h(t), where c is a real parameter, a(t), b(t) and h(t) are continuous T-periodic functions. [...]
2019 - 10.12150/jnma.2019.167
Journal of Nonlinear Modeling and Analysis, Vol. 1, Issue 2 (June 2019) , p. 167-177  
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9.
16 p, 342.0 KB Periodic solutions of the Duffing differential equation revisited via the averaging theory / Benterki, Rebiha (Université de Bordj Bou Arréridj. Département de Mathématiques (Algeria)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We use three different results of the averaging theory of first order for studying the existence of new periodic solutions in the two Duffing differential equations ¨ y + asiny = bsint and ¨ y + ay−cy3 = bsint, where a, b and c are real parameters.
2019 - 10.12150/jnma.2019.11
Journal of Nonlinear Modeling and Analysis, Vol. 1, Issue 1 (March 2019) , p. 11-26  
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10.
27 p, 592.4 KB Phase portraits of quadratic polynomial differential systems having as solution some classical planar algebraic curves of degree 4 / Benterki, Rebiha (Université Bachir El Ibrahimi. Département de Mathématiques (Algeria)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We classify the phase portraits of quadratic polynomial differential systems having some relevant classic quartic algebraic curves as invariant algebraic curves, i. e. these curves are formed by solution curves of a quadratic polynomial differential system. [...]
2019
Electronic journal of differential equations, Vol. 2019, Issue 15 (2019) , p. 1-25
2 documentos
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