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UAB Digital Repository of Documents 785 records found  1 - 10nextend  jump to record: Search took 0.04 seconds. 
1.
Study of the Nonelementary Singular Points and the Dynamics Near the Infinity in Predator-Prey Systems / Diz-Pita, Érika (Universidade de Santiago de Compostela) ; Llibre, Jaume (Universitat Autònoma de Barcelona) ; Otero-Espinar, M. Victoria (Universidade de Santiago de Compostela)
In this chapter, we present the results obtained in two predator-prey systems, paying special attention to the dynamics near the infinity and the nonelementary singular points. First, the desingularization technique known as blow-up technique allows one to study any type of singularities of analytic systems in dimension two even if they are not elementary. [...]
Cham : Springer, 2023 (Nonlinear Systems and Complexity ; 38) - 10.1007/978-3-031-42689-6_5
Computational and Mathematical Models in Biology, 2023, p. 103-128  
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2.
9 p, 290.7 KB Dynamics of the Isotropic Star Differential System from the Mathematical and Physical Point of Views / Artés Ferragud, Joan Carles (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Vulpe, Nicolae (Vladimir Andrunakievichi Institute of Mathematics and Computer Science (Moldova))
The following differential quadratic polynomial differential system dx/dt=y−x, dy/dt=2y−y/y−1(2−yy−5y−4/y−1x), when the parameter y∈(1,2] models the structure equations of an isotropic star having a linear barotropic equation of state, being x=m(r)/r where m(r)≥0 is the mass inside the sphere of radius r of the star, y=4πr2ρ where ρ is the density of the star, and t=ln(r/R) where R is the radius of the star. [...]
2024 - 10.3390/appliedmath4010004
AppliedMath, Vol. 4, Issue 1 (January 2024) , p. 70-78  
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3.
20 p, 971.1 KB Planar central configurations of some restricted (4 + 1)-body problems / Corbera Subirana, Montserrat (Universitat de Vic - Universitat Central de Catalunya. Departament d'Enginyeries) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemàtica)
We start with the 13 central configurations of the restricted (4 + 1) body problem having four primaries with equal masses at the vertices of a square. Then, we describe the evolution of these central configurations when some of the masses of the four primaries tend to zero and the remainder ones keep constant. [...]
2022 - 10.1063/5.0091642
Journal of Mathematical Physics, Vol. 63, Issue 12 (December 2022) , art. 122901  
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4.
10 p, 616.4 KB Integrability and dynamics of a simplified class B laser system / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Pantazi, Chara (Universitat Politècnica de Catalunya. Departament de Matemàtiques)
A simplified class B laser system is a family of differential polynomial systems of degree two depending on the parameters a and b. Its rich dynamics has already been observed in 1980s, see Arecchi et al. [...]
2023 - 10.1063/5.0169342
Chaos, Vol. 33, Issue 10 (October 2023) , art. 103119  
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5.
22 p, 1.3 MB Existence of a cylinder foliated by periodic orbits in the generalized Chazy differential equation / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Novaes, Douglas D. (Universidade Estadual de Campinas. Instituto de Matemática, Estatística e Computação Científica. Departamento de Matemática) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática)
The generalized Chazy differential equation corresponds to the following two-parameter family of differential equations x ⃛ + | x | q x ¨ + k | x | q x x ˙ 2 = 0, which has its regularity varying with q, a positive integer. [...]
2023 - 10.1063/5.0138309
Chaos, Vol. 33, Issue 7 (July 2023) , art. 73104  
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6.
On the periodic orbits of the continuous-discontinuous piecewise differential systems with three pieces separated by two parallel straight lines / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Teixeira, Marco Antonio (Universidade Estadual de Campinas. Departamento de Matemática)
During these last twenty years many papers have been published about the piecewise differential systems in the plane. The increasing interest on these kind of differential systems mainly is due to their big number of applications for modeling many natural phenomena. [...]
2023 - 10.1016/j.cnsns.2023.107421
Communications in nonlinear science and numerical simulation, Vol. 125 (October 2023) , art. 107421  
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7.
19 p, 300.3 KB An extension of the 16th Hilbert problem for continuous piecewise linear-quadratic centers separated by a non-regular line / Esteban, Marina (Universidad de Córdoba. Departamento de Informática y Análisis Numérico) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento Matemática)
In the last few decades, there has been much interest in studying piecewise differential systems. This is mainly due to the fact that these differential systems allow us to modelize many natural phenomena. [...]
2023 - 10.1063/5.0167089
Chaos, Vol. 33, Issue 12 (December 2023) , art. 123120  
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8.
17 p, 3.2 MB Phase portraits on the unit sphere of the stretch-twist-fold flow / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemàtica)
The so-called stretch-twist-fold flow consists in a Stokes flow depending on two parameters defined in a unit closed ball B¯ that is associated with the motion of a fluid particle coming from the dynamo theory, and it models a mechanism for studying the magnetic field of the Earth and the Sun. [...]
2023 - 10.15388/namc.2023.28.33088
Nonlinear Analysis: Modelling and Control, Vol. 28, Issue 5 (September 2023) , p. 1020-1036  
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9.
Polynomial differential systems with hyperbolic limit cycles / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemàtica)
One of the main problems of the qualitative theory of the planar differential equations is the study their limit cycles. In this paper given an algebraic curve of degree n we characterize the planar polynomial differential systems of degree greater or equal than n which admit the ovals of the algebraic curve as hyperbolic limit cycles.
2023 - 10.1016/j.geomphys.2023.104983
Journal of geometry and physics, Vol. 194 (December 2023) , art. 104983  
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10.
The limit cycles of a class of piecewise differential systems / Benabdallah, Imane (University Mohamed El Bachir. Department of Mathematics) ; Benterki, Rebiha (University Mohamed El Bachir. Department of Mathematics) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this century many papers have been published on the piecewise differential systems in the plane. The increasing interest for this class of differential systems is motivated by their many applications for modelling several natural phenomena. [...]
2023 - 10.1007/s40590-023-00535-x
Boletin de la Sociedad Matematica Mexicana, Vol. 29, Issue 3 (November 2023) , art. 62  
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