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17 p, 655.4 KB

Dynamics and Darboux integrability of the D 2 polynomial vector fields of degree 2 in ℝ3 / Ginoux, Jean-Marc (Centre National de la Recherche Scientifique. Université de Toulon. Centre de Physique Théorique (France)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática (Portugal))
We characterize the Darboux integrability and the global dynamics of the 3-dimensional polynomial differential systems of degree 2 which are invariant under the D2 symmetric group, which have been partially studied previously by several authors.
2021 - DOI (Digital Object Identifier)

10.1007/s11040-020-09372-0
Mathematical Physics, Analysis and Geometry, Vol. 24, Issue 1 (March 2021) , art. 1

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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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11 p, 628.1 KB

Darboux polynomials, balances and Painlevé property / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática)
For a given polynomial differential system we provide different necessary conditions for the existence of Darboux polynomials using the balances of the system and the Painlevé property. As far as we know, these are the first results which relate the Darboux theory of integrability, first, to the Painlevé property and, second, to the Kovalevskaya exponents. [...]
2017 - DOI (Digital Object Identifier)

10.1134/S1560354717050057
Regular and Chaotic Dynamics, Vol. 22, Issue 5 (September 2017) , p. 543-550

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10 p, 661.5 KB

On the integrability of Hamiltonian systems with d degrees of freedom and homogenous polynomial potential of degree n / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade Técnica de Lisboa. Instituto Superior Técnico. Departamento de Matemática)
We consider Hamiltonian systems with d degrees of freedom and a Hamiltonian of the form H = 1/2 d∑i=1 p21+V(q1,. . . ,qd), where V is a homogenous polynomial of degree n ≥ 3. We prove that such Hamiltonian systems with n odd or n = 4m, have a Darboux first integral if and only if they have a polynomial first integral.
2018 - DOI (Digital Object Identifier)

10.1142/S0219199717500456
Communications in Contemporary Mathematics, Vol. 20, Issue 8 (December 2018) , art. 1750045

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23 p, 338.8 KB

Conservation laws in biochemical reaction networks / Mahdi, Adam (University of Oxford. Institute of Biomedical Engineering. Department of Engineering Science) ; Ferragut Amengual, Antoni Manel (Universitat Jaume I. Institut Universitari de Matemàtiques i Aplicacions de Castelló) ; Valls, Clàudia 1973- (Instituto Superior Técnico. Departamento de Matemática (Portugal)) ; Wiuf, Carsten (University of Copenhagen. Department of Mathematical Sciences)
We study the existence of linear and nonlinear conservation laws in biochemical reaction networks with mass-action kinetics. It is straightforward to compute the linear conservation laws as they are related to the left null-space of the stoichiometry matrix. [...]
2017 - DOI (Digital Object Identifier)

10.1137/17M1138418
SIAM Journal on Applied Dynamical Systems, Vol. 16, Issue 4 (2017) , p. 2213-2232

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21 p, 459.5 KB

On the computation of Darboux first integrals of a class of planar polynomial vector fields / Ferragut Amengual, Antoni Manel (Universitat Jaume I. Institut Universitari de Matemàtiques i Aplicacions de Castelló) ; Galindo, Carlos (Universitat Jaume I. Institut Universitari de Matemàtiques i Aplicacions de Castelló) ; Monserrat, Francisco (Universitat Politècnica de València. Institut Universitari de Matemàtica Pura i Aplicada)
We study the class of planar polynomial vector fields admitting Darboux first integrals of the type ∏ri = 1fαii, where the αi's are positive real numbers and the fi's are polynomials defining curves with only one place at infinity. [...]
2019 - DOI (Digital Object Identifier)

10.1016/j.jmaa.2019.05.052
Journal of mathematical analysis and applications, Vol. 478, Issue 2 (October 2019) , p. 743-763

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13 p, 678.3 KB

On the Darboux integrability of the logarithmic galactic potentials / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática)
We study the logarithmic Hamiltonians H=(p +p )∕2+log(1+x+y∕q), which appear in the study of the galactic dynamics. We characterize all the invariant algebraic hypersurfaces and all exponential factors of the Hamiltonian system with Hamiltonian H. [...]
2017 - DOI (Digital Object Identifier)

10.1016/j.geomphys.2017.07.019
Journal of geometry and physics, Vol. 121 (November 2017) , p. 279-287

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14 p, 712.2 KB

Liouvillian first integrals for a class of generalized Liénard polynomial differential systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Departamento de Matemática)
We study the existence of Liouvillian first integrals for the generalized Liénard polynomial differential systems of the form x' = y, y' =-g(x)-f(x)y, where f(x) = 3Q(x)Q'(x)P(x) + Q(x) P'(x) and g(x) = Q(x)Q'(x)(Q(x) P(x)-1) with P,Q [x]. [...]
2016 - DOI (Digital Object Identifier)

10.1017/S0308210515000906
Proceedings of the Royal Society of Edinburgh Section A: Mathematics, Vol. 146, Issue 6 (December 2016) , p. 1195-1210

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13 p, 731.7 KB

On the Darboux integrability of the Hindmarsh-Rose burster / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade Técnica de Lisboa. Departamento de Matemática)
We study the HindmarshRose burster which can be described by the differential system x?=y?x3+bx2+I?z,y?=1?5x2?y,z?=?(s(x?x0)?z), where b, I, ?, s, x0 are parameters. We characterize all its invariant algebraic surfaces and all its exponential factors for all values of the parameters. [...]
2018 - DOI (Digital Object Identifier)

10.1007/s10114-017-5661-1
Acta Mathematica Sinica. English Series, Vol. 34, issue 6 (2018) , p. 947-958

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10.

14 p, 708.3 KB

On the integrability of the 5-dimensional Lorenz system for the gravity-wave activity / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Departamento de Matemàtica)
We consider the 5-dimensional Lorenz system \[ U' &= -V W b V Z, \\ V' &= UW-b UZ, \\ W'&= -U V,\\ X' &= -Z, \\ Z'&=b UV X \] where b \R \0\ and the derivative is with respect to T. [...]
2017 - DOI (Digital Object Identifier)

10.1090/proc/13233
Proceedings of the American Mathematical Society, Vol. 145 Núm. 2 (2017) , p. 665-679

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