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UAB Digital Repository of Documents 8 records found  Search took 0.01 seconds. 
1.
58 p, 6.6 MB Phase Portraits of a Class of Continuous Piecewise Linear Differential Systems / Li, Jie (Southwest Petroleum University. School of Sciences) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
The phase portraits of the planar linear differential systems are very well known. This is not the case for the phase portraits of the planar continuous piecewise linear differential systems. In this paper we classify the phase portraits of the class of planar continuous piecewise linear differential systems of the form x˙=a|x|+by+c,y˙=α|x|+βy+γ, in the Poincaré disc when aβ- bα≠ 0, and prove the existence and uniqueness of limit cycles. [...]
2023 - 10.1007/s12591-023-00666-7
Differential Equations and Dynamical Systems, (November 2023)  
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2.
On the connection between global centers and global injectivity in the plane / Braun, Francisco (Universidade Federal de São Carlos. Departamento de Matemática) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this note we revisit a result of Sabatini relating global injectivity of polynomial maps to global centers in the plane. We deliver a generalization of this result for C maps defined on connected sets. [...]
2023 - 10.1007/s12591-023-00630-5
Differential Equations and Dynamical Systems, (July 2023)  
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3.
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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4.
8 p, 295.0 KB 4-dimensional zero-Hopf bifurcation for polynomial differentials systems with cubic homogeneous nonlinearities via averaging theory / Feddaoui, Amina (University of Annaba. Department of Mathematics (Algeria)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Makhlouf, Ammar (University of Annaba. Department of Mathematics (Algeria))
The averaging theory of second order shows that for polynomial differential systems in ℝ4 with cubic homogeneous nonlinearities at least nine limit cycles can be born in a zero-Hopf bifurcation.
2020 - 10.1504/IJDSDE.2020.109106
International Journal of Dynamical Systems and Differential Equations, Vol. 10, Issue 4 (2020) , p. 321-328  
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5.
6 p, 759.9 KB Periodic solutions for a class of non-autonomous Newton differential equations / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Makhlouf, Ammar (University of Annaba. Department of Mathematics (Algeria))
We provide sufficient conditions for the existence of periodic solutions of the second-order non-autonomous differential equation x¨=-∇xV(t,x),in R, where V(t,x)=‖x‖22+εW(t,x) with W(t, x) a 2 π-periodic function in the variable t, ε is a small parameter, x∈ R and ∇xV(t,x)=(∂V∂x1,…,∂V∂xn). [...]
2016 - 10.1007/s12591-016-0333-7
Differential Equations and Dynamical Systems, (October 2016)  
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6.
8 p, 630.9 KB Zero-Hopf Periodic Orbit of a Quadratic System of Differential Equations Obtained from a Third-Order Differential Equation / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Makhlouf, Ammar (University of Annaba (Algèria). Department of Mathematics)
We study the zero-Hopf bifurcation of the third-order differential equations x″'+(a1x+a0)x″+(b1x+b0)x'+x2=0,where a, a , b and b are real parameters. The prime denotes derivative with respect to an independent variable t. [...]
2019 - 10.1007/s12591-017-0375-5
Differential Equations and Dynamical Systems, Vol. 27, Issue 1-3 (January 2019) , p. 75-82  
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7.
12 p, 370.0 KB Piecewise bounded quadratic systems in the plane / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; da Silva, Clayton Eduardo Lente (UNESP(Brazil). Deparatamento de Matemática) ; Da Silva, Paulo R. (UNESP(Brazil). Deparatamento de Matemática)
In this paper we study the sliding mode of piecewise bounded quadratic systems in the plane given by a non-smooth vector field Z = (X, Y ). Analyzing the singular, crossing and sliding sets, we get the conditions which ensure that any solution, including the sliding one, is bounded.
2014 - 10.1007/s12591-014-0205-y
Differential Equations and Dynamical Systems, 2014  
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8.
7 p, 318.1 KB A Note on Forced Oscillations in Differential Equations with Jumping Nonlinearities / Buica, Adriana (Bolyai University. Department of Mathematics) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Makarenkov, Oleg (University of Texas at Dallas. Department of Mathematical Sciences)
The goal of this paper is to study bifurcations of asymptotically stable 2-periodic solutions in the forced asymmetric oscillator u c u u a u^ =1 t by means of a Lipschitz generalization of the second Bogolubov's theorem due to the authors. [...]
2015 - 10.1007/s12591-014-0199-5
Differential Equations and Dynamical Systems, Vol. 23 Núm. 4 (2015) , p. 415-421  
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