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Dipòsit Digital de Documents de la UAB	7 registres trobats	La cerca s'ha fet en 0.01 segons.

25 p, 748.9 KB

On the integrability of a tritrophic food chain model / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Instituto Superior Técnico. Departamento de Matemática (Portugal))
In this paper we work with a vastly analyzed tritrophic food chain model. We provide a complete characterization of their Darboux polynomials and of their exponential factors. We also show the non-existence of polynomial first integrals, of rational first integrals, of local analytic first integrals in a neighborhood of the origin, of first integrals that can be described by formal series and of Darboux first integrals.
2010 - DOI (Digital Object Identifier)

10.1515/ans-2010-0206
Advanced Nonlinear Studies, Vol. 10, Issue 2 (May 2010) , p. 331-355

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7 p, 678.5 KB

Polynomial solutions of equivariant polynomial Abel differential equations / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática)
Let a(x) be non-constant and let bj(x), for j = 0, 1, 2, 3, be real or complex polynomials in the variable x. Then the real or complex equivariant polynomial Abel differential equation a(x)y = b(x)y + b(x)y, with b(x) =/ 0, and the real or complex polynomial equivariant polynomial Abel differential equation of the second kind a(x)yy = b0(x) + b(x)y, with b(x) =/ 0, have at most 7 polynomial solutions. [...]
2018 - DOI (Digital Object Identifier)

10.1515/ans-2017-6043
Advanced Nonlinear Studies, Vol. 18, Issue 3 (August 2018) , p. 537-542

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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 - DOI (Digital Object Identifier)

10.1515/ans-2017-6033
Advanced Nonlinear Studies, Vol. 18, issue 1 (2018) , p. 183-193

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25 p, 401.8 KB

Limit cycles coming from some uniform isochronous centers / Liang, Haihua (Guangdong Polytechnic Normal University(China). Department of Computer Science) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
This article is about the weak 16--th Hilbert problem, i. e. we analyze how many limit cycles can bifurcate from the periodic orbits of a given polynomial differential center when it is perturbed inside a class of polynomial differential systems. [...]
2016 - DOI (Digital Object Identifier)

10.1515/ans-2015-5010
Advanced Nonlinear Studies, Vol. 16 Núm. 2 (2016) , p. 197-220

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9 p, 757.4 KB

Liouvillian first integrals for generalized Liénard 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 Liouvillian first integrals for the generalized Liénard polynomial differential systems of the form x' = y, y' = −g(x) − f(x)y, where g(x) and f(x) are arbitrary polynomials such that 2 ≤ deg g ≤ deg f.
2013 - DOI (Digital Object Identifier)

10.1515/ans-2013-0404
Advanced Nonlinear Studies, Vol. 13 (2013) , p. 819-829

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15 p, 344.9 KB

Limit cycles bifurcating from a 2-dimensional isochronous torus in R^3 / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper we illustrate the explicit implementation of a method for computing limit cycles which bifurcate from a 2-dimensional isochronous set contained in ℝ3, when we perturb it inside a class of differential systems. [...]
2011 - DOI (Digital Object Identifier)

10.1515/ans-2011-0208
Advanced Nonlinear Studies, Vol. 11 (2011) , p. 377-389

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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 - DOI (Digital Object Identifier)

10.1515/ans-2015-0411
Advanced Nonlinear Studies, Vol. 15 (2015) , p. 951-961

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