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UAB Digital Repository of Documents 64 records found  1 - 10nextend  jump to record: Search took 0.01 seconds. 
1.
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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2.
19 p, 718.1 KB Counting configurations of limit cycles and centers / Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Guillamon, Antoni (Universitat Politècnica de Catalunya. Departament de Matemàtiques) ; Mañosa Fernández, Víctor 1971- (Universitat Politècnica de Catalunya. Departament de Matemàtiques)
We present several results on the determination of the number and distribution of limit cycles or centers for planar systems of differential equations. In most cases, the study of a recurrence is one of the key points of our approach. [...]
2023 - 10.56415/basm.y2023.i1.p78
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica., Vol. 101, Issue 1 (2023) , p. 78-96  
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3.
Nilpotent Bicenters in Continuous Piecewise Z2 -Equivariant Cubic Polynomial Hamiltonian Vector Fields : Cusp-Cusp Type / Chen, Ting (Guangdong University of Finance and Economics. School of Statistics and Mathematics) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper, we study the global dynamics for a class of continuous piecewise Z2-equivariant cubic Hamiltonian vector fields with nilpotent bicenters at (±1, 0). We consider these polynomial vector fields with a challenging case where the bicenters (±1, 0) come from the combination of two nilpotent cusps separated by y = 0. [...]
2023 - 10.1142/S0218127423501389
International journal of bifurcation and chaos in applied sciences and engineering, Vol. 33, Issue 12 (September 2023) , art. 2350138  
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4.
13 p, 959.5 KB Symmetric Phase Portraits of Homogeneous Polynomial Hamiltonian Systems of Degree 1, 2, 3, 4, and 5 with Finitely Many Equilibria / Benterki, Rebiha (University Mohamed El Bachir El Ibrahimi. Department of Mathematics) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Roughly speaking, the Poincaré disc D2 is the closed disc centered at the origin of the coordinates of R2, where the whole of R2 is identified with the interior of D2 and the circle of the boundary of D2 is identified with the infinity of R2, because in the plane R2, we can go to infinity in as many directions as points have the circle. [...]
2023 - 10.3390/sym15081476
Symmetry, Vol. 15, Issue 8 (August 2023) , art. 1476  
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5.
58 p, 6.6 MB Phase Portraits of a Class of Continuous Piecewise Linear Differential Systems / Li, Jie (Southwest Petroleum University. School of Sciences) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
The phase portraits of the planar linear differential systems are very well known. This is not the case for the phase portraits of the planar continuous piecewise linear differential systems. In this paper we classify the phase portraits of the class of planar continuous piecewise linear differential systems of the form x˙=a|x|+by+c,y˙=α|x|+βy+γ, in the Poincaré disc when aβ- bα≠ 0, and prove the existence and uniqueness of limit cycles. [...]
2023 - 10.1007/s12591-023-00666-7
Differential Equations and Dynamical Systems, (November 2023)  
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6.
52 p, 2.1 MB Global phase portraits of the quadratic systems having a singular and irreducible invariant curve of degree 3 / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Pantazi, Chara (Universitat Politècnica de Catalunya. Departament de Matemàtiques)
Any singular irreducible cubic curve (or simply, cubic) after an affine transformation can be written as either y2 = x3, or y2 = x2(x + 1), or y2 = x2(x - 1). We classify the phase portraits of all quadratic polynomial differential systems having the invariant cubic y2 = x2(x + 1). [...]
2023 - 10.1142/S0218127423500037
International journal of bifurcation and chaos in applied sciences and engineering, Vol. 33, Issue 1 (January 2023) , art. 2350003  
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7.
14 p, 1.1 MB Planar Kolmogorov systems with infinitely many singular points at infinity / Diz-Pita, Érika (Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Otero-Espinar, M. Victoria (Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización)
We classify the global dynamics of the five-parameter family of planar Kolmogorov systems y˙ = y (b0 + b1yz + b2y + b3z), z˙ = z (c0 + b1yz + b2y + b3z), which is obtained from the Lotka-Volterra systems of dimension three. [...]
2022 - 10.1142/S0218127422500651
International journal of bifurcation and chaos in applied sciences and engineering, Vol. 32, Issue 5 (April 2022) , art. 2250065  
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8.
18 p, 887.5 KB Nilpotent bi-center in continuous piecewise Z2-equivariant cubic polynomial Hamiltonian systems / Chen, Ting (Guangdong University of Finance and Economics. School of Statistics and Mathematics) ; Li, Shimin (Guangdong University of Finance and Economics. School of Statistics and Mathematics) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
One of the classical and difficult problems in the theory of planar differential systems is to classify their centers. Here we classify the global phase portraits in the Poincaré disk of the class continuous piecewise differential systems separated by one straight line and formed by two cubic Hamiltonian systems with nilpotent bi-center at (± 1, 0). [...]
2022 - 10.1007/s11071-022-07631-z
Nonlinear Dynamics, Vol. 110, Issue 1 (September 2022) , p. 705-721  
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9.
16 p, 409.5 KB Phase portraits of the Selkov model in the Poincaré disc / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Nabavi, Arefeh (Isfahan University of Technology. Department of Mathematical Sciences (Iran))
In this paper we classify the phase portraits in the Poincaré disc of the Selkov model for the glycolysis process x˙ = −x + ay + x2y, y˙ = b − ay − x2y, in function of its parameters a, b ∈ R. [...]
2022 - 10.3934/dcdsb.2022056
Discrete and Continuous Dynamical Systems - B, Vol. 27, Issue 12 (December 2022) , p. 7607-7623  
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10.
24 p, 1.3 MB Nilpotent center in a continuous piecewise quadratic polynomial Hamiltonian vector field / Chen, Ting (Guangdong University of Finance and Economics. School of Statistics and Mathematics (China)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper, we study the global dynamics of continuous piecewise quadratic Hamiltonian systems separated by the straight line x = 0, where these kinds of systems have a nilpotent center at (0, 0), which comes from the combination of two cusps of both Hamiltonian systems. [...]
2022 - 10.1142/S0218127422501164
International journal of bifurcation and chaos in applied sciences and engineering, Vol. 32, Issue 8 (June 2022) , art. 2250116  
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