GSD Seminar - 2023/1
GSD SEMINAR - 2023/1
Organizer: Prof. João Medrado
Seminar 1
April 25, 2023
Speaker: Prof. Oscar Alexander Ramírez Cespedes (UFV)
Departamento de Matemática, Universidade Federal de Viçosa, 74001–970 Viçosa, Minas Gerais, Brazil.
Email address: oscar.ramirez@ufv.br
Title: Local behaviour near degenerate two-fold singularities
Abstract: Our main aim is to study the local dynamics near singularities of piecewise smooth dynamical systems on R^3, the so-called degenerate two-fold singularities. More specifically, we are interested in discussing the existence of invariant manifolds around these singularities. Co–authors: Rony Cristiano and Otávio Gomide.
Time: 10:00 GMT-3
Virtual Room: meet.google.com/fvg-pmit-xud
Seminar 2
May 2, 2023
Speaker: Prof. Rony Cristiano (UFG)
Title: Global stability of a Lotka-Volterra piecewise-smooth system with two predators competing for one prey
Auditório do IME / 10:00 GMT-3
Seminar 3
May 9, 2023
Speaker: Johana Jeidy Jimenez Ruiz - UFOB/UAB (Spain)
Title: Limit cycles for discontinuous piecewise differential systems in R3 separated by a quadric
Virtual Room: meet.google.com/fvg-pmit-xud
10:00 GMT-3
Seminar 4
May 16, 2023
Speaker: Tiago de Carvalho - FFCLRP/USP
Title: Entropy for Non-Smooth Vector Fields
Abstract: Non-smooth vector fields does not have necessarily the property of uniqueness of solution passing through a point and this is responsible to enrich the behavior of the system. Even on the plane non-smooth vector fields can be chaotic, a feature impossible for the smooth or continuous case. In this work we set the ground for one to begin the study of entropy for non-smooth vector fields. We construct a metric space of all possible trajectories of a non-smooth vector field, where we define a flow inherited by the vector field and then define the topological entropy in this scenario. As a consequence, we are able to obtain some general results of this theory and give some examples of planar non-smooth vector fields with positive (finite and infinite) entropy.
10:00 GMT-3
Auditório IME/UFG
Virtual Room: meet.google.com/fvg-pmit-xud
Seminar 5
May 23, 2023
Speaker: Lucyjane de Almeida Silva
Title: Codimension-two singularities of Constrained systems on R3
Abstract: See Full Abstract
10:00 GMT-3
Auditório IME/UFG
Virtual Room: meet.google.com/fvg-pmit-xud
Seminar 6
May 30, 2023
Speaker: Marina Tuyako Mizukoshi - IME/UFG
Title: PVI com incerteza generalizada com aplicação a modelos epidemiológicos.
Abstract: Nesta apresentação será introduzida o conceito de teoria intervalar utilizando CI (constraint interval) com aplicações em sistemas dinâmicos. Em particular em modelos utilizando dados da COVID no Brasil e nos Estados Unidos.
Referências:
[1] CECCONELLO, M.S. ; MIZUKOSHI, M.T. ; LODWICK, W. . Interval nonlinear initial-valued problem using constraint intervals: Theory and an application to the Sars-Cov-2 outbreak. INFORMATION SCIENCES, v. 577, p. 871-882, 2021.
[2] Marina T. Mizukoshi; LODWICK, W. A. . The Constraint Interval Theory: A Solution for Interval Differential Equations. In: Scott Dick, Vladik Kreinovich, Pawan Lingras. (Org.). Applications of Fuzzy Techniques. 1ed.Estados Unidos: Springer International Publishing, 2022, v. 500, p. 148-159.
10:00 GMT-3
Auditório IME/UFG
Seminar 7
June 6, 2023
Speaker: Luiz Fernando Gonçalves - IME/UFG
Title: Limit cycles on piecewise smooth vector fields with coupled rigid centers.
Abstract: Investigaremos o número máximo de ciclos limite de classes de sistemas diferenciais descontínuos por partes no plano formados por dois sistemas separados por uma linha reta, e assumindo que cada um desses sistemas diferenciais tem um centro rígido e são compostos por uma parte linear e uma parte não linear polinomial homogênea. Para este tipo de sistemas diferenciais descontínuos, investigaremos o 16º problema de Hilbert.
10:00 GMT-3
Auditório IME/UFG
Seminar 8
June 13, 2023
Speaker: Ronaldo Alves Garcia - IME/UFG
Title: Equações diferenciais de segunda ordem aplicadas a problemas de geometria diferencial equivariante.
Abstract: Nesse seminário faremos uma análise qualitativa de equações diferenciais de segunda ordem provenientes de hipersuperfícies de curvatura média constante em Rn possuindo simetrias dos grupos ortogonais O(n-1) e O(p)xO(q), p+q=n-1. Exemplos específicos serão apresentados.
10:00 GMT-3
Auditório IME/UFG
Seminar 9
June 20, 2023
Speaker: Ewerton Rocha Vieira - Rutgers University - USA/IME-UFG
Title: Extracting Dynamics from Sparse Data
Abstract: We present a novel approach that enables the characterization of specific local and/or global dynamic behavior in a stationary deterministic nonlinear dynamical system, even with sparse data. We demonstrate how our method can successfully capture various dynamic features such as fixed points, periodic orbits, connecting orbits, bistability, and chaotic dynamics.
Time: 10:00 GMT-3
Virtual Room: meet.google.com/fvg-pmit-xud
Seminar 10
June 27, 2023
Speaker: Letícia Cândido - IMECC/Unicamp
Title: Sliding Shilnikov Orbit: theoretical aspects and applications in biological systems
Abstract:
This work is inspired by the work of Shilnikov in (1, 2). An interesting behavior can be observed in smooth vector fields, where a trajectory connects an equilibrium point to itself, which we call homoclinic orbit. Shilnikov studied a special kind of homoclinic orbit and the behavior of the vector field close to it. Since the study of piecewise smooth vector fields is of our interest, we are going to generalize the definition of homoclinic orbit for the piecewise context. Using this, we can study the behavior close to this orbit and prove a chaotic of the trajectories.
Keywords: Sliding Shilnikov Orbit, Piecewise Vector Field, Bernoulli Shift, Chaos.
References
1 AFRAIMOVICH, V. S.; NIKOV, L. P. S. Strange attractors and quasiattractors. In: Nonlinear dynamics and turbulence. [S.l.]: Pitman, Boston, MA, 1983, (Interaction Mech. Math. Ser.). p. 1–34. ISBN 0-273-08560-3. páginas
2 NIKOV, L. P. Šil. Existence of a countable set of periodic motions in a neighborhood of a homoclinic curve. Dokl. Akad. Nauk SSSR, p. 298–301, 1967. ISSN 0002-3264. páginas
3 NOVAES, D. D.; TEIXEIRA, M. A. Shilnikov problem in Filippov dynamical systems. Chaos, v. 29, n. 6, p. 063110, 8, 2019. ISSN 1054-1500,1089-7682. Disponível em: . páginas
4 NOVAES, D. D.; PONCE, G.; aO, R. V. Chaos induced by sliding phenomena in Filippov systems. J. Dynam. Differential Equations, v. 29, n. 4, p. 1569– 1583, 2017. ISSN 1040-7294,1572-9222. Disponível em: . páginas
5 GUARDIA, M.; SEARA, T. M.; TEIXEIRA, M. A. Generic bifurcations of low codimension of planar Filippov systems. J. Differential Equations, v. 250, n. 4, p. 1967– 2023, 2011. ISSN 0022-0396,1090-2732. Disponível em: . páginas
6 DUMORTIER, F.; LLIBRE, J.; ARTéS, J. C. Qualitative theory of planar differential systems. [S.l.]: Springer-Verlag, 2 Berlin, 2006. xvi+298 p. (Universitext). ISBN 3-540-32893-9. páginas
7 SOTOMAYOR, J. Generic bifurcations of dynamical systems. In: Dynamical systems (Proc. Sympos., Univ. Bahia, Salvador, 1971),. [S.l.]: „ 1973. p. 561–582. páginas
8 SOTOMAYOR, J. Lições de equações diferenciais ordinárias. [S.l.]: Instituto de Matemática Pura e Aplicada, Rio de Janeiro„, 1979. xvi+327 p. páginas
Time: 10:00 GMT-3
Virtual Room: meet.google.com/fvg-pmit-xud
Seminar 11
July 4, 2023
Speaker: Samuel Carlos de S. Ferreira - UFG
Title: Existência de ciclos limites para uma classe de campos lineares por partes em R3 com tangências quadráticas
Abstract: See Full Abstract
10:00 GMT-3
Auditório IME/UFG
Seminar 12
July 18, 2023
Speaker: Luiz Fernando Gouveia - IBILCE/UNESP
Title: Holomorphic slow-fast systems
Abstract: In this work, we are concerned with studying the existence of invariant complex manifolds of two-dimensional holomorphic systems. From the geometric theory of singular perturbations we know that if a slow-fast system has associated a normally hyperbolic compact critical manifold, then there exists a smooth locally invariant manifold. However, this smooth manifold does not necessarily have a complex structure. Here, we provide conditions to guarantee the existence of one-dimensional invariant complex manifolds. Consequently, this allows us to establish that the centers, foci, and nodes of the reduced problem are persistent by singular perturbation. The tools used by us are the usual techniques of Fenichel and Briot-Bouquet Theories.
10:00 GMT-3
Virtual Room: meet.google.com/fvg-pmit-xud
Seminar 13
July 25, 2023
Speaker: Paulo Santana - IBILCE/UNESP
Title: On polynomial perturbation of polycycles
Abstract: See Full Abstract
10:00 GMT-3
Virtual Room: meet.google.com/fvg-pmit-xud
Seminar 14
August 1, 2023
Speaker: Weldon A. Lodwick - University of Colorado Denver and Visiting Professor, Universidade Federal do Ceará
Title: The Interval Uncertainty Eigenvalue Problem via the Optimization of the Constraint Interval Representation
10:00 GMT-3
Auditório IME/UFG
Seminar 15
August 8, 2023
Speaker: Angela Carolina Tunubalá Sánchez - IME/UFG
Title: Equivalência entre o Método de Melnikov e o Método de Averaging
Auditório do IME / 10:00 GMT-3
Seminar 16
August 15, 2023
Speaker: Yovani Adolfo Villanueva Herrera - IME/UFG
Title: A geometric proof of Bautin theorem
Abstract: We are going to review the main ideas of Dulac, Bautin and Roussarie for providing a maximum number for the cyclicity of elliptic singular points of quadratic vector fields on the real plane, analysing the Taylor coefficients of the Poincaré map and using some methods of algebraic geometry.
10:00 GMT-3
Virtual Room: meet.google.com/fvg-pmit-xud
Seminar 17
August 22, 2023
Speaker: Warley Mendes Batista - IME/UFG
Title: Singularidades de codimensão zero e um de Campos Vetoriais Suaves por Partes Planares Reversíveis
Auditório do IME / 10:00 GMT-3