UAB Digital Repository of Documents 21 records found  1 - 10nextend  jump to record: Search took 0.00 seconds. 
1.
52 p, 1.1 MB Quadratic systems with an invariant algebraic curve of degree 3 and a Darboux invariant / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Oliveira, Regilene (Universidade de São Paulo. Instituto de Ciências Matemáticas e Computação) ; Rodrigues, Camila A. B. (Universidade Federal de Santa Catarina. Departamento de Matemática (Brazil))
Let QS be the class of non-degenerate planar quadratic differential systems and QS3 its subclass formed by the systems possessing an invariant cubic f(x, y) = 0. In this article, using the action of the group of real affine transformations and time rescaling on QS, we obtain all the possible normalforms for the quadratic systems in QS3. [...]
2021
Electronic journal of differential equations, Vol. 2021, Issue 69 (2021) , p. 1-52
2 documents
2.
6 p, 264.2 KB On the limit cycle of a Belousov-Zhabotinsky differential systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Oliveira, Regilene (Universidade de São Paulo. Instituto de Ciências Matemáticas e Computação.)
In Leonov and Kuznetsov (2013), the authors shown numerically the existence of a limit cycle surrounding the unstable node that system (1) has in the positive quadrant for specific values of the parameters. [...]
2022 - 10.1002/mma.7798
Mathematical methods in the applied sciences, Vol. 45, Issue 2 (January 2022) , p. 579-584  
3.
20 p, 337.0 KB First-order perturbation for multi-parameter center families / Itikawa, Jackson (Universidade Federal de Rondônia. Departament of Mathematics) ; Oliveira, Regilene (Universidade de São Paulo. Departamento de Matemática) ; Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In the weak 16th Hilbert problem, the Poincaré-Pontryagin-Melnikov function, M(h), is used for obtaining isolated periodic orbits bifurcating from centers up to a first-order analysis. This problem becomes more difficult when a family of centers is considered. [...]
2022 - 10.1016/j.jde.2021.11.035
Journal of differential equations, Vol. 309 (February 2022) , p. 291-310  
4.
35 p, 542.0 KB Simultaneous Bifurcation of Limit Cycles and Critical Periods / Oliveira, Regilene (Universidade de São Paulo. Departamento de Matemática) ; Sanchez Sanchez, Ivan (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
The present work introduces the problem of simultaneous bifurcation of limit cycles and critical periods for a system of polynomial differential equations in the plane. The simultaneity concept is defined, as well as the idea of bi-weakness in the return map and the period function. [...]
2022 - 10.1007/s12346-021-00546-x
Qualitative theory of dynamical systems, Vol. 21, Issue 1 (March 2022) , art. 20  
5.
22 p, 833.4 KB On the birth and death of algebraic limit cycles in quadratic differential systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Oliveira, Regilene (Universidade de São Paulo. Instituto de Ciências Matemáticas e Computação. Departamento de Matemática (Brazil)) ; Zhao, Yulin (Sun Yat-sen University. School of Mathematics (People's Republic of China))
In 1958 started the study of the families of algebraic limit cycles in the class of planar quadratic polynomial differential systems. In the present we known one family of algebraic limit cycles of degree 2 and four families of algebraic limit cycles of degree 4, and that there are no limit cycles of degree 3. [...]
2021 - 10.1017/S0956792520000145
European Journal of Applied Mathematics, Vol. 32, Issue 2 (April 2021) , p. 317-336  
6.
49 p, 872.3 KB Structurally unstable quadratic vector fields of codimension two : families possessing either a cusp point or two finite saddle-nodes / Artés Ferragud, Joan Carles (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Oliveira, Regilene (Universidade de São Paulo. Instituto de Ciências Matemáticas e de Computação (Brazil)) ; Rezende, Alex C. (Universidade Federal de São Carlos. Departamento de Matemática (Brazil))
The goal of this paper is to contribute to the classification of the phase portraits of planar quadratic differential systems according to their structural stability. Artés et al. (Mem Am Math Soc 134:639, 1998) proved that there exist 44 structurally stable topologically distinct phase portraits in the Poincaré disc modulo limit cycles in this family, and Artés et al. [...]
2020 - 10.1007/s10884-020-09871-2
Journal of dynamics and differential equations, vol. 33 (July 2020) p. 1779-1821  
7.
129 p, 4.9 MB Geometric and algebraic classification of quadratic differential systems with invariant hyperbolas / Oliveira, Regilene (Universidade de São Paulo. Instituto De Ciências Matemáticas e de Computação) ; Rezende, Alex C. (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Schlomiuk, Dana (Université de Montréal. Département de Mathématiques et de Statistiques) ; Vulpe, Nicolae (Academy of Sciences of Moldova. Institute of Mathematics and Computer Science)
Let QSH be the whole class of non-degenerate planar quadratic differential systems possessing at least one invariant hyperbola. We classify this family of systems, modulo the action of the group of real affine transformations and time rescaling, according to their geometric properties encoded in the configurations of invariant hyperbolas and invariant straight lines which these systems possess. [...]
2017
Electronic journal of differential equations, Vol. 2017, Issue 295 (2017) , p. 1-122
2 documents
8.
53 p, 809.9 KB Family of quadratic differential systems with invariant hyperbolas: a complete classification in the space R12 / Oliveira, Regilene (Universidade de São Paulo. Instituto De Ciências Matemáticas e de Computação) ; Rezende, Alex C. (Universidade de São Paulo. Instituto De Ciências Matemáticas e de Computação) ; Vulpe, Nicolae (Academy of Sciences of Moldova. Institute of Mathematics and Computer Science)
In this article we consider the class QS of all non-degenerate quadratic systems. A quadratic polynomial differential system can be identified with a single point of R12 through its coefficients. In this paper using the algebraic invariant theory we provided necessary and sufficient conditions for a system in QS to have at least one invariant hyperbola in terms of its coefficients. [...]
2016
Electronic journal of differential equations, Vol. 2016, Issue 162 (2016) , p. 1-50
2 documents
9.
16 p, 666.6 KB Limit cycles for two classes of control piecewise linear differential systems / 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)) ; Rodrigues, Camila A. B. (Universidade Federal de Santa Catarina. Departamento de Matemática (Brazil))
We study the bifurcation of limit cycles from the periodic orbits of 2n-dimensional linear centers x˙ = A0x when they are perturbed inside classes of continuous and discontinuous piecewise linear differential systems of control theory of the form x˙ = A0x+ ε(Ax+ ϕ(x) b), where ϕ is a continuous or discontinuous piecewise linear function, A0 is a 2n×2n matrix with only purely imaginary eigenvalues, ε is a small parameter, A is an arbitrary 2n×2n matrix, and b is an arbitrary vector of Rn.
2020 - 10.1007/s40863-020-00163-7
São Paulo Journal of Mathematical Sciences, Vol. 14, Issue 1 (June 2020) , p. 49-65  
10.
14 p, 332.1 KB Limit cycles in uniform isochronous centers of discontinuous differential systems with four zones / Itikawa, Jackson (Universidade de São Paulo. Instituto de Ciências Matemáticas e de Computação. Departamento de Matemática (Brazil)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Mereu, Ana Cristina (Universidade Federal de São Carlos. Departamento de Física, Química e Matemática (Brazil)) ; Oliveira, Regilene (Universidade de São Paulo. Instituto de Ciências Matemáticas e de Computação. Departamento de Matemática (Brazil))
We apply the averaging theory of first order for discontinuous differential systems to study the bifurcation of limit cycles from the periodic orbits of the uniform isochronous center of the differential systems ẋ = -y+x, y = x + xy, and ẋ = -y + xy, y = x + xy, when they are perturbed inside the class of all discontinuous quadratic and cubic polynomials differential systems with four zones separately by the axes of coordinates, respectively. [...]
2017 - 10.3934/dcdsb.2017136
Discrete and continuous dynamical systems. Series B, Vol. 22, Issue 9 (November 2017) , p. 3259-3272  

UAB Digital Repository of Documents : 21 records found   1 - 10nextend  jump to record:
See also: similar author names
2 Oliveira, R.
3 Oliveira, Rafael S.
20 Oliveira, Regilene
3 Oliveira, Regilene Delazari dos Santos,
1 Oliveira, Roni Ivan Rocha
1 Oliveira, Ronielton Rezende
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