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Articles 83 registres trobats  anterior11 - 20següentfinal  anar al registre: La cerca s'ha fet en 0.02 segons. 
11.
12 p, 781.7 KB Limit cycles of a perturbation of a polynomial Hamiltonian systems of degree 4 symmetric with respect to the origin / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Martínez, Y. Paulina (Universidad del Bío-Bío. Departamento de Matemática (Chile)) ; Vidal, Claudio (Universidad del Bío-Bío. Departamento de Matemática (Chile))
We study the number of limit cycles bifurcating from the origin of a Hamiltonian system of degree 4. We prove, using the averaging theory of order 7, that there are quartic polynomial systems close these Hamiltonian systems having 3 limit cycles.
2020 - 10.4153/S0008439519000626
Canadian mathematical bulletin, Vol. 63, Issue 3 (September 2020) , p. 547-561  
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12.
13 p, 535.8 KB Global phase portraits of a predator-prey system / Diz-Pita, Érika (Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Otero-Espinar, M. Victoria (Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización)
We classify the global dynamics of a family of Kolmogorov systems depend-ing on three parameters which has ecological meaning as it modelizes a predator-prey system. We obtain all their topologically distinct global phase portraits in the positive quadrant of the Poincaré disc, so we provide all the possible distinct dynamics of these systems.
2022 - 10.14232/ejqtde.2022.1.16
Electronic Journal of Qualitative Theory of Differential Equations, Vol. 2022, Issue 16 (2022) , p. 1-13
2 documents
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13.
10 p, 681.8 KB Dynamics of the Szekeres system / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemàtica)
The Szekeres model is a differential system in R4 that provides the solutions of the Einstein field equations in the presence of irrotational dust. This differential system is integrable with two rational first integrals and one analytic first integral. [...]
2021 - 10.1063/5.0054051
Journal of Mathematical Physics, Vol. 62, Issue 8 (August 2021) , art. 82502  
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14.
38 p, 850.7 KB Phase portraits of a family of Kolmogorov systems depending on six parameters / Diz-Pita, Érika (Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Otero Espinar, Maria Victoria (Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización)
We consider a general 3-dimensional Lotka-Volterra system with a rational first integral of degree two of the form H = xi yj zk. The restriction of this Lotka-Volterra system to each surface H(x, y, z) = h varying h ∈ R provide Kolmogorov systems. [...]
2021
Electronic journal of differential equations, Vol. 2021, Issue 35 (2021) , p. 1-38
2 documents
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15.
52 p, 1.1 MB Quadratic systems with an invariant algebraic curve of degree 3 and a Darboux invariant / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Oliveira, Regilene (Universidade de São Paulo. Instituto de Ciências Matemáticas e Computação) ; Rodrigues, Camila A. B. (Universidade Federal de Santa Catarina. Departamento de Matemática (Brazil))
Let QS be the class of non-degenerate planar quadratic differential systems and QS3 its subclass formed by the systems possessing an invariant cubic f(x, y) = 0. In this article, using the action of the group of real affine transformations and time rescaling on QS, we obtain all the possible normalforms for the quadratic systems in QS3. [...]
2021
Electronic journal of differential equations, Vol. 2021, Issue 69 (2021) , p. 1-52
2 documents
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16.
29 p, 1.1 MB Phase portraits of separable quadratic systems and a bibliographical survey on quadratic systems / Li, Tao (Sichuan University. Department of Mathematics) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Although planar quadratic differential systems and their applications have been studied in more than one thousand papers, we still have no complete understanding of these systems. In this paper we have two objectives. [...]
2021 - 10.1016/j.exmath.2021.01.003
Expositiones Mathematicae, Vol. 39, Issue 4 (December 2021) , p. 540-565  
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17.
Hamiltonian nilpotent saddles of linear plus cubic homogeneous polynomial vector fields / Corbera Subirana, Montserrat (Universitat de Vic - Universitat Central de Catalunya) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemàtica)
We completely characterize the global phase portraits in the Poincaré disk for all planar Hamiltonian vector fields with linear plus cubic homogeneous terms having a nilpotent saddle at the origin.
2022 - 10.1016/j.nonrwa.2021.103451
Nonlinear Analysis: Real World Applications, Vol. 64 (April 2022) , art. 103451  
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18.
20 p, 3.2 MB Phase portraits of a family of Kolmogorov systems with infinitely many singular points at infinity / Diz-Pita, Érika (Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Otero Espinar, Maria Victoria (Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización)
We give the topological classification of the global phase portraits in the Poincaré disc of the Kolmogorov systems ẋ=xa+cx+cz+cz, ż=zc+cx+cz+cz, which depend on five parameters and have infinitely many singular points at the infinity. [...]
2022 - 10.1016/j.cnsns.2021.106038
Communications in nonlinear science and numerical simulation, Vol. 104 (January 2022) , art. 106038  
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19.
28 p, 867.8 KB Phase portraits of (2;0) reversible vector fields with symmetrical singularities / Buzzi, Claudio (Universidade Estadual Paulista Júlio de Mesquita Filho. Instituto de Biociências, Letras e Ciências Exatas) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Santana, Paulo (Universidade Estadual Paulista Júlio de Mesquita Filho. Instituto de Biociências, Letras e Ciências Exatas)
In this paper we study the phase portraits in the Poincaré disk of the reversible vector fields of type (2;0) having generic bifurcations around a symmetric singular point p. We also prove the nonexistence of any periodic orbit surrounding p. [...]
2021 - 10.1016/j.jmaa.2021.125324
Journal of mathematical analysis and applications, Vol. 503, Issue 2 (November 2021) , art. 125324  
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20.
89 p, 1.8 MB Structurally unstable quadratic vector fields of codimension two : Families possessing a finite saddle-node and an infinite saddle-node / Artés Ferragud, Joan Carles (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Mota, Marcos Coutinho (Universidade de São Paulo. Instituto de Ciências Matemáticas e de Computação (Brazil)) ; Rezende, Alex C. (Universidade Federal de São Carlos. Departamento de Matemática (Brazil))
In 1998, Artés, Kooij and Llibre proved that there exist 44 structurally stable topologically distinct phase portraits modulo limit cycles, and in 2018 Artés, Llibre and Rezende showed the existence of at least 204 (at most 211) structurally unstable topologically distinct codimension-one phase portraits, modulo limit cycles. [...]
2021 - 10.14232/ejqtde.2021.1.35
Electronic Journal of Qualitative Theory of Differential Equations, Vol. 2021, Issue 35 (2021) , p. 1-89
2 documents
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Articles : 83 registres trobats   anterior11 - 20següentfinal  anar al registre:
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