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UAB Digital Repository of Documents 13 records found  1 - 10next  jump to record: Search took 0.01 seconds. 
1.
17 p, 725.3 KB On the global dynamics of a three-dimensional forced-damped differential system / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Martínez, Y. Paulina (Centre de Recerca Matemàtica) ; Valls, Clàudia 1973- (Universidade Técnica de Lisboa. Instituto Superior Técnico. Departamento de Matemática (Portugal))
In this paper by using the Poincaré compactification of ℝ³ we make a global analysis of the model xʹ = ax + y + yz, yʹ = x - ay + bxz, zʹ = cz - bxy. In particular we give the complete description of its dynamics on the infinity sphere. [...]
2020 - 10.1080/14029251.2020.1757232
Journal of Nonlinear Mathematical Physics, Vol. 27, Issue 3 (May 2020) , p. 414-428  
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2.
13 p, 4.1 MB Global dynamics of a Lotka-Volterra system in ℝ³ / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Martínez, Y. Paulina (Centre de Recerca Matemàtica) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemàtica (Portugal))
In this work we consider the Lotka-Volterra system in R³ x˙ = −x(x − y − z), y˙ = −y(−x + y − z), z˙ = −z(−x − y + z), introduced recently in [7], and studied also in [8] and [14]. [...]
2020 - 10.1080/14029251.2020.1757240
Journal of Nonlinear Mathematical Physics, Vol. 27, Issue 3 (May 2020) , p. 509-519  
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3.
11 p, 382.4 KB Final evolutions of a class of May-Leonard Lotka-Volterra systems / Buzzi, Claudio (Universidade Estadual Paulista. Departamento de Matemática (Brazil)) ; Santos, Robson A. T. (Universidade Estadual Paulista. Departamento de Matemática (Brazil)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We study a particular class of Lotka-Volterra 3-dimensional systems called May-Leonard systems, which depend on two real parameters a and b, when a + b = −1. For these values of the parameters we shall describe its global dynamics in the compactification of the non-negative octant of ℝ3 including its infinity. [...]
2020 - 10.1080/14029251.2020.1700635
Journal of Nonlinear Mathematical Physics, Vol. 27, Issue 2 (January 2020) , p. 267-278  
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4.
22 p, 232.4 KB On the Darboux integrability of a three-dimensional forced-damped differential system / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Oliveira, Regilene (Universidade de São Paulo. Instituto De Ciências Matemáticas e de Computação. Departamento de Matemática (Brazil)) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática)
In 2011 Pehlivan proposed a three-dimensional forced-damped autonomous differential system which can display simultaneously unbounded and chaotic solutions. This untypical phenomenon has been studied recently by several authors. [...]
2017 - 10.1080/14029251.2017.1375686
Journal of Nonlinear Mathematical Physics, Vol. 24, Issue 4 (September 2017) , p. 473-494  
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5.
12 p, 699.2 KB Proper rational and analytic first integrals for asymmetric 3-dimensional Lotka-Volterra systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Departamento de Matematica)
We go beyond in the study of the integrability of the classical model of competition between three species studied by May and Leonard [19], by considering a more realistic asymmetric model. Our results show that there are no global analytic first integrals and we provide all proper rational first integrals of this extended model by classifying its invariant algebraic surfaces.
2017 - 10.1080/14029251.2017.1341701
Journal of Nonlinear Mathematical Physics, Vol. 24 Núm. 3 (2017) , p. 393-404  
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6.
13 p, 702.2 KB Weierstrass integrability for a class of differential systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade Técnica de Lisboa. Departamento de Matemática)
We characterize the differential equations of the form x' = y, y' = an(x)yn + an−1(x)yn−1 + · · · + a1(x)y + a0(x), n ≥ 2, an(0) ̸= 0, where aj (x) are meromorphic functions in the variable x for j = 0, . [...]
2014 - 10.1080/14029251.2014.915165
Journal of Nonlinear Mathematical Physics, Vol. 21 Núm. 2 (2014) , p. 294-307  
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7.
12 p, 646.9 KB Darboux integrability of a generalized Friedmann-Robertson-Walker Hamiltonian system / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade Técnica de Lisboa. Departamento de Matemática)
We study the Darboux first integrals of a generalized Friedmann-Robertson-Walker Hamiltonian system.
2013 - 10.1080/14029251.2013.854482
Journal of Nonlinear Mathematical Physics, Vol. 20 Núm. 3 (2013) , p. 394-406  
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8.
7 p, 708.4 KB Liouvillian and analytic first integrals for the Brusselator system / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade Técnica de Lisboa. Departamento de Matemática)
We characterize the Liouvillian and analytic first integrals for the polynomial differential systems of the form x' = a − (b + 1)x + x2y, y' = bx − x2y, with a, b ∈ R, called the Brusselator differential systems.
2012 - 10.1142/S1402925112500167
Journal of Nonlinear Mathematical Physics, Vol. 19 Núm. 2 (2012) , p. 8 pp.  
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9.
8 p, 469.1 KB On the integrability of a Muthuswamy-Chua system / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Departamento de Matematica)
2012 - 10.1142/S1402925112500295
Journal of Nonlinear Mathematical Physics, Vol. 19 Núm. 4 (2012) , p. 1250029 (12 pages)  
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10.
11 p, 609.9 KB Darboux integrability of a simplified Friedmann-Robertson-Walker Hamiltonian system / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Departamento de Matematica)
2012 - 10.1142/S1402925112500362
Journal of Nonlinear Mathematical Physics, Vol. 19, Núm. 4 (2012) , p. 607-617  
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