UAB Digital Repository of Documents 14 records found  1 - 10next  jump to record: Search took 0.02 seconds. 
1.
31 p, 607.7 KB On the cyclicity of Kolmogorov polycycles / Marín Pérez, David (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Villadelprat Yagüe, Jordi (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Centre de Recerca Matemàtica
In this paper we study planar polynomial Kolmogorov's differential systems Xμ{x˙=f(x,y;μ),y˙=g(x,y;μ), with the parameter μ varying in an open subset Λ⊂RN. Compactifying Xμ to the Poincaré disc, the boundary of the first quadrant is an invariant triangle Γ, that we assume to be a hyperbolic polycycle with exactly three saddle points at its vertices for all μ∈Λ. [...]
2022 - 10.14232/ejqtde.2022.1.35
Electronic Journal of Qualitative Theory of Differential Equations, Vol. 35 (2022) , p. 1-31  
2.
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
3.
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 documents
4.
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
5.
22 p, 816.7 KB Period function of planar turning points / Huzak, Renato (Hasselt University. Campus Diepenbeek (Belgium)) ; Rojas, David (Universitat de Girona. Departament d'Informàtica, Matemàtica Aplicada i Estadística)
This paper is devoted to the study of the period function of planar generic and non-generic turning points. In the generic case (resp. non-generic) a non-degenerate (resp. degenerate) center disappears in the limit ɛ → 0, where ɛ ≥ 0 is the singular perturbation parameter. [...]
2021 - 10.14232/ejqtde.2021.1.16
Electronic Journal of Qualitative Theory of Differential Equations, Vol. 2021, Issue 16 (2021) , p. 1-21
2 documents
6.
34 p, 471.7 KB Stability index of linear random dynamical systems / Cimà, Anna (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Mañosa Fernández, Víctor 1971- (Universitat Politècnica de Catalunya. Departament de Matemàtiques)
Given a homogeneous linear discrete or continuous dynamical system, its stability index is given by the dimension of the stable manifold of the zero solution. In particular, for the n dimensional case, the zero solution is globally asymptotically stable if and only if this stability index is n. [...]
2021 - 10.14232/ejqtde.2021.1.15
Electronic Journal of Qualitative Theory of Differential Equations, Vol. 2021, Issue 15 (2021) , p. 1-27
2 documents
7.
46 p, 2.6 MB Crossing limit cycles for piecewise linear differential centers separated by a reducible cubic curve / Jimenez, Jeidy J. (Universidade Federal do Oeste da Bahia (Brasil)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Medrado, Joao Carlos (Universidade Federal de Goiás. Instituto de Matemática e Estatística (Brasil))
As for the general planar differential systems one of the main problems for the piecewise linear differential systems is to determine the existence and the maximum number of crossing limits cycles that these systems can exhibit. [...]
2020 - 10.14232/ejqtde.2020.1.19
Electronic Journal of Qualitative Theory of Differential Equations, Vol. 2020, Issue 19 (2020) , p. 1-48
2 documents
8.
19 p, 716.5 KB Strongly formal weierstrass non-integrability for polynomial differential systems in C2 / Giné, Jaume (Universitat de Lleida. Departament de Matemàtica) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Recently a criterion has been given for determining the weakly formal Weierstrass non-integrability of polynomial differential systems in C2. Here we extend this criterion for determining the strongly formal Weierstrass non-integrability which includes the weakly formal Weierstrass non-integrability of polynomial differential systems in C2. [...]
2020 - 10.14232/ejqtde.2020.1.1
Electronic Journal of Qualitative Theory of Differential Equations, Vol. 2020, Issue 1 (2020) , p. 1-16
2 documents
9.
13 p, 299.6 KB On a Class of Invariant Algebraic Curves for Kukles Systems / Osuna, Osvaldo (UMSNH(México). Instituto de Física y Matemáticas) ; Rebollo-Perdomo, Salomón (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Villaseñor, Gabriel (Instituto Tecnológico de Morelia(México). Departamento de Ciencias Básicas)
In this paper we give a new upper bound for the degree of a class of transversal to infinity invariant algebraic curves for polynomial Kukles systems of arbitrary degree. Moreover, we prove that a quadratic Kukles system having at least one transversal to infinity invariant algebraic curve is integrable.
2016 - 10.14232/ejqtde.2016.1.61
Electronic Journal of Qualitative Theory of Differential Equations, Vol. 61 (2016) , p. 1-12  
10.
12 p, 363.9 KB Analytic reducibility of nondegenerate centers: Cherkas systems / Giné, Jaume (Universitat de Lleida. Departament de Matemàtica) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper we study the center problem for polynomial differential systems and we prove that any center of an analytic differential system is analytically reducible. We also study the centers for the Cherkas polynomial differential systems x˙ = y, y˙ = P0(x) + P1(x)y + P2(x)y2, where Pi(x) are polynomials of degree n, P0(0) = 0 and P'0(0) < 0. [...]
2016 - 10.14232/ejqtde.2016.1.49
Electronic Journal of Qualitative Theory of Differential Equations, Vol. 49 (2016) , p. 1-10  

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