UAB Digital Repository of Documents 8 records found  Search took 0.02 seconds. 
1.
The centers and their cyclicity for a class of polynomial differential systems of degree 7 / Benterki, Rebiha (Université Bachir El Ibrahimi. Département de Mathématiques (Algeria)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We classify the global phase portraits in the Poincaré disc of the generalized Kukles systems ẋ=−y,ẏ=x+axy6+bx3y4+cx5y2+dx7,which are symmetric with respect to both axes of coordinates. Moreover using the averaging theory up to sixth order, we study the cyclicity of the center located at the origin of coordinates, i. [...]
2020 - 10.1016/j.cam.2019.112456
Journal of computational and applied mathematics, Vol. 368 (April 2020) , art. 112456  
2.
18 p, 507.4 KB Limit cycles of continuous and discontinuous piecewise-linear differential systems in R³ / De Freitas, Bruno R. (Universidade Federal de Goiás. Instituto de Matemática e Estatística) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Medrado, Joao Carlos (Universidade Federal de Goiás. Instituto de Matemática e Estatística)
We study the limit cycles of two families of piecewise-linear differential systems in R³ with two pieces separated by a plane Ʃ. In one family the differential systems are only continuous on the plane Ʃ, and in the other family they are only discontinuous on the plane Ʃ. [...]
2018 - 10.1016/j.cam.2018.01.028
Journal of computational and applied mathematics, Vol. 338 (Aug. 2018) , p. 311-323  
3.
8 p, 341.6 KB Uniform isochronous cubic and quartic centers: Revisited / Artés, Joan Carles (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Itikawa, Jackson (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper we completed the classification of the phase portraits in the Poincaré disc of uniform isochronous cubic and quartic centers previously studied by several authors. There are three and fourteen different topological phase portraits for the uniform isochronous cubic and quartic centers respectively.
2017 - 10.1016/j.cam.2016.09.018
Journal of computational and applied mathematics, Vol. 313 (2017) , p. 448-453  
4.
16 p, 437.4 KB Centers and limit cycles of polynomial differential systems of degree 4 via averaging theory / Benterki, Rebiha (Centre Universitaire de Bordj Bou Arréridj(Algeria). Département de Mathématiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper we classify the phase portraits in the Poincar\'e disc of the centers of the generalized class of Kukles systems \[ =-y,=x ax^3y bxy^3, \] symmetric with respect to the y-axis, and we study, using the averaging theory up to sixth order, the limit cycles which bifurcate from the periodic solutions of these centers when we perturb them inside the class of all polynomial differential systems of degree 4.
2017 - 10.1016/j.cam.2016.08.047
Journal of computational and applied mathematics, Vol. 313 (2017) , p. 273-283  
5.
7 p, 327.4 KB A note on the equilibria of an economic model with local competition ''à la Cournot'' / Guirao, Juan Luis Garcia (Universidad Politécnica de Cartagena. Departamento de Matemática Aplicada y Estadística) ; López, Miguel Angel (Universidad de Castilla-La Mancha. Departamento de Matemáticas) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Martínez, Raquel (Universidad de Castilla-La Mancha. Departamento de Matemáticas)
Guirao and Rubio (2010) [12] introduce an economic model, which generalizes the classical duopoly of Cournot type, where the competitors are located around a circle or a line and each firm competes ''à la Cournot'' with its right and left neighboring. [...]
2012 - 10.1016/j.cam.2010.11.030
Journal of computational and applied mathematics, Vol. 236 (2012) , p. 3052-3057  
6.
19 p, 771.0 KB Centers and isochronous centers for generalized quintic systems / Giné, Jaume (Universitat de Lleida. Departament de Matemàtica) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade Técnica de Lisboa. Departamento de Matemática)
In this paper we classify the centers and the isochronous centers of certain polynomial differential systems in R2 of degree d ≥ 5 odd that incomplex notation can be written as z˙ = (λ + i)z + (zz¯)d−52 (Az5 + Bz4z¯ + Cz3z¯2 + Dz2z¯3 + Ezz¯4 + Fz¯5),where λ ∈ R and A, B, C, D, E, F ∈ C. [...]
2015 - 10.1016/j.cam.2014.11.007
Journal of computational and applied mathematics, Vol. 279 (2015) , p. 173-186  
7.
36 p, 790.3 KB Limit cycles for continuous and discontinuous perturbations of uniform isochronous cubic centers / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Itikawa, Jackson (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Let p be a uniform isochronous cubic polynomial center. We study the maximum number of small or medium limit cycles that bifurcate from p or from the periodic solutions surrounding p respectively, when they are perturbed, either inside the class of all continuous cubic polynomial differential systems, or inside the class of all discontinuous differential systems formed by two cubic differential systems separated by the straight line y = 0. [...]
2015 - 10.1016/j.cam.2014.09.007
Journal of computational and applied mathematics, Vol. 277 (2015) , p. 171-191  
8.
23 p, 433.4 KB Phase portraits of uniform isochronous quartic centers / Itikawa, Jackson (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper we classify the global phase portraits in the Poincaré disc of all quartic polynomial differential systems with a uniform isochronous center at the origin such that their nonlinear part is not homogeneous.
2015 - 10.1016/j.cam.2015.02.046
Journal of computational and applied mathematics, Vol. 287 (2015) , p. 98-114  

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