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Results overview: Found 10 records in 0.02 seconds.
Articles, 10 records found
Articles 10 records found  
1.
17 p, 570.2 KB Normal forms and global phase portraits of quadratic and cubic integrable vector fields having two nonconcentric circles as invariant algebraic curves / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Messias, Marcelo (Universidade Estadual Paulista. Departamento de Matemática e Computação (Brazil)) ; Reinol, Alisson C. (Universidade Estadual Paulista. Departamento de Matemática e Computação (Brazil))
In this paper, we give the normal form of all planar polynomial vector fields of degree d ≤ 3 having two nonconcentric circles C and C as invariant algebraic curves and the function H=C C , with α and β real values, as first integral. [...]
2017 - 10.1080/14689367.2016.1263600
Dynamical Systems, Vol. 32, Issue 3 (2017) , p. 374-390  
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2.
17 p, 590.0 KB The cubic polynomial differential systems with two circles as algebraic limit cycles / Giné, Jaume (Universitat de Lleida. Departament de Matemàtica) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Departamento de Matemàtica)
In this paper we characterize all cubic polynomial differential systems in the plane having two circles as invariant algebraic limit cycles.
2018 - 10.1515/ans-2017-6033
Advanced Nonlinear Studies, Vol. 18, issue 1 (2018) , p. 183-193  
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3.
14 p, 331.7 KB Global phase portraits of quadratic systems with a complex ellipse as invariant algebraic curve / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Departamento de Matemàtica)
In this paper we study a new class of quadratic systems and classify all its phase portraits. More precisely, we characterize the class of all quadratic polynomial differential systems in the plane having a complex ellipse x^2 y^2 1=0 as invariant algebraic curve. [...]
2018 - 10.1007/s10114-017-5478-y
Acta Mathematica Sinica. English Series, Vol. 34, issue 5 (2018) , p. 801-811  
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4.
21 p, 1.9 MB Quantitative analysis of competition models / Chiralt, Cristina (Universitat Jaume I. Departament de Matemàtiques) ; Ferragut Amengual, Antoni Manel (Universitat Jaume I. Departament de Matemàtiques) ; Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Vindel, Pura (Universitat Jaume I. Departament de Matemàtiques)
We study a 2-species Lotka-Volterra type differential system, modeling competition between two species and having a coexistence equilibrium in the first quadrant. In case that this equilibrium is of saddle type, its stable manifold divides the first quadrant into two zones. [...]
2017 - 10.1016/j.nonrwa.2017.06.001
Nonlinear Analysis: Real World Applications, Vol. 38 (2017) , p. 327-347  
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5.
10 p, 766.6 KB Algebraic invariant curves and first integrals for Riccati polynomial differential systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade Técnica de Lisboa. Departamento de Matemática)
We characterize the algebraic invariant curves for the Riccati polynomial differential systems of the form x' = 1, y' = a(x)y2 +b(x)y +c(x), where a(x), b(x) and c(x) are arbitrary polynomials. We also characterize their algebraic first integrals.
2014 - 10.1090/S0002-9939-2014-12085-5
Proceedings of the American Mathematical Society, Vol. 142 Núm. 10 (2014) , p. 3533-3543  
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6.
8 p, 300.9 KB Non-algebraic oscillations for predator-prey models / Ferragut Amengual, Antoni Manel (Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I) ; Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We prove that the limit cycle oscillations of the celebrated Rosenzweig-MacArthur differential system and other predator-prey models are non-algebraic.
2014 - 10.5565/PUBLMAT_Extra14_11
Publicacions matemàtiques, Vol. Extra (2014) , p. 195-207
2 documents
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7.
12 p, 727.4 KB On the extensions of the Darboux theory of integrability / Giné, Jaume (Universitat de Lleida. Departament de Matemàtica) ; Grau, Maite (Universitat de Lleida. Departament de Matemàtica) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Recently some extensions of the classical Darboux integrability theory to autonomous and non-autonomous polynomial vector fields have been done. The classical Darboux integrability theory and its recent extensions are based on the existence of algebraic invariant hypersurfaces. [...]
2013 - 10.1088/0951-7715/26/8/2221
Nonlinearity, Vol. 26 Núm. 8 (2013) , p. 2221-2229  
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8.
16 p, 625.7 KB Liouvillian first integrals of quadratic-linear polynomial differential systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Instituto Superior Técnico (Lisboa). Departamento de Matemática)
For a large class of quadratic-linear polynomial differential systems with a unique singular point at the origin having non-zero eigenvalues, we classify the ones which have a Liouvillian first integral, and we provide the explicit expression of them.
2011 - 10.1016/j.jmaa.2010.12.033
Journal of mathematical analysis and applications, Vol. 379 (2011) , p. 188-199  
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9.
9 p, 736.5 KB Liouvillian first integrals for generalized Riccati polynomial differential systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade Técnica de Lisboa. Departamento de Matemática)
We study the existence and non-existence of Liouvillian first integrals for the generalized Riccati polynomial differential systems of the form x'=y, y'= a(x)y^2 b(x)y c(x), where a(x), b(x) and c(x) are polynomials.
2015 - 10.1515/ans-2015-0411
Advanced Nonlinear Studies, Vol. 15 (2015) , p. 951-961  
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10.
28 p, 497.5 KB A class of polynomial planar vector fields with polynomial first integral / Ferragut Amengual, Antoni Manel (Universitat Jaume I. Departament de Matemàtiques) ; Galindo, Carlos (Universitat Jaume I. Departament de Matemàtiques) ; Monserrat, Francisco (Universitat Politècnica de València. E.T.S. d'Informatica Aplicada)
2015 - 10.1016/j.jmaa.2015.04.062
Journal of mathematical analysis and applications, Vol. 430 (2015) , p. 354-380  
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