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12 p, 287.8 KB |
Twin Quadratic Polynomial Vector Fields in the Space C3
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Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ;
Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática)
In this paper we study quadratic polynomial vector fields on C3 with 8 isolated singularities. Either two polynomial vector fields share six singularities with the same position and spectra and the remaining two singularities have some relation on their spectra, or two polynomial vector fields share five singularities with the same position and spectra and the remaining three singularities have some other relation on their spectra. [...]
2024
Dynamics of continuous, discrete and impulsive systems, Vol. 31, Issue 2 (2024) , p. 121-132
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2024-09-20 18:54 |
6 p, 248.5 KB |
Dynamics of a class of 3-dimensional Lotka-Volterra Systems
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Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ;
Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática)
We provide the complete dynamics of the Lotka-Volterra differential system x˙ = x(ay − cz), y˙ = y(bz − ax), z˙ = z(cx − by), where a, b, c are positive parameters and x, y, z are in the positive octant of R3. [...]
2023
Dynamics of continuous, discrete and impulsive systems, Vol. 30, Issue 4 (2023) , p. 303-307
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2024-09-17 11:39 |
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Topological entropy, sets of periods, and transitivity for circle maps
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Alsedà i Soler, Lluís (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ;
Bordignon, Liane (Universidade Federal de São Carlos. Departamento de Matemática) ;
Groisman, Jorge (Universidad de la República. Instituto de Matemática y Estadística Rafael Laguardia)
Transitivity, the existence of periodic points and positive topological entropy can be used to characterize complexity in dynamical systems. It is known that for graphs that are not trees, for every ε > 0, there exist (complicate) totally transitive maps (then with cofinite set of periods) such that the topological entropy is smaller than ε (simplicity). [...]
2024 - 10.1007/s11253-024-02305-y
Ukrainian Mathematical Journal, Vol. 76, Issue 1 (June 2024) , p. 31-50
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Limit cycles of discontinuous piecewise differential Hamiltonian systems separated by a circle, or a parabola, or a hyperbola
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Casimiro, Joyce A. (Universidade Estadual de Campinas. Departamento de Matemática) ;
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Piecewise differential systems in the plane have been extensively studied in the last two decades, due to the vast application of these systems to describe natural phenomena. The knowledge of the existence or not of periodic solutions, in particular, of the limit cycles, is very important for understanding the dynamics of the differential systems. [...]
2024 - 10.1016/j.matcom.2024.05.021
Mathematics and computers in simulation, Vol. 225 (November 2024) , p. 303-312
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