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UAB Digital Repository of Documents 146 records found  1 - 10nextend  jump to record: Search took 0.02 seconds. 
1.
Critical periods in planar polynomial centers near a maximum number of cusps / De Maesschalck, Peter (Hasselt University) ; Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We provide the best lower bound for the number of critical periods of planar polynomial centers known up to now. The new lower bound is obtained in the Hamiltonian class and considering a single period annulus. [...]
2024 - 10.1016/j.jde.2023.10.034
Journal of differential equations, Vol. 380 (January 2024) , p. 181-197  
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2.
24 p, 449.0 KB Probability of existence of limit cycles for a family of planar systems / Coll, Bartomeu (Universitat de les Illes Balears. Departament de Ciències Matemàtiques i Informàtica) ; Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Prohens, Rafel (Universitat de les Illes Balears. Departament de Ciències Matemàtiques i Informàtica)
The goal of this work is the study of the probability of occurrence of limit cycles for a family of planar differential systems that are a natural extension of linear ones. To prove our results we first develop several results of non-existence, existence, uniqueness and non-uniqueness of limit cycles for this family. [...]
2023 - 10.1016/j.jde.2023.07.015
Journal of differential equations, Vol. 373 (November 2023) , p. 152-175  
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3.
47 p, 945.5 KB Characterization for stability in planar conductivities / Faraco, Daniel (Universidad Autónoma de Madrid. Departamento de Matemáticas) ; Prats, Martí (Universidad Autónoma de Madrid. Departamento de Matemáticas)
We find a complete characterization for sets of uniformly strongly elliptic and isotropic conductivities with stable recovery in the L2 norm when the data of the Calderón Inverse Conductivity Problem is obtained in the boundary of a disk and the conductivities are constant in a neighborhood of its boundary. [...]
2018 - 10.1016/j.jde.2018.01.013
Journal of differential equations, Vol. 264, Issue 9 (May 2018) , p. 5659-5712  
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4.
Invariants of polynomial vector fields / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemàtica)
We characterize the existence of first integrals and invariants (first integrals depending on the time) for the polynomial vector fields which are invariant under an involution.
2023 - 10.1016/j.jde.2023.05.024
Journal of differential equations, Vol. 365 (August 2023) , p. 895-904  
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5.
Global centers of the generalized polynomial Liénard differential systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemàtica)
The global centers started to be studied seriously at the end of the XX century. In the last decades, the generalized polynomial Liénard differential systems have been studied intensively. In this paper we characterize all the generalized polynomial Liénard differential systems having a global center at the origin. [...]
2022 - 10.1016/j.jde.2022.05.013
Journal of differential equations, Vol. 330 (September 2022) , p. 66-80  
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6.
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  
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7.
79 p, 1.0 MB The criticality of reversible quadratic centers at the outer boundary of its period annulus / Marín Pérez, David (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Villadelprat Yagüe, Jordi (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques) ; Centre de Recerca Matemàtica
This paper deals with the period function of the reversible quadratic centers where . Compactifying the vector field to , the boundary of the period annulus has two connected components, the center itself and a polycycle. [...]
2022 - 10.1016/j.jde.2022.05.026
Journal of differential equations, Vol. 332 (Sep. 2022) , p. 123-201  
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8.
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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9.
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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10.
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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