Institute of Mathematics and Statistics - Federal University of Goiás
Contact info:
euzebio at ufg dot br - Office 228 +55 62 3521 1153
Jacarandá street, Campus Samambaia, CP 74690-900, Goiânia, Goiás, Brazil
Welcome! Here is a brief bio: I completed my undergraduate and graduate studies at São Paulo State University under the supervision of Prof. Claudio A. Buzzi. I stayed about a year during my doctorate studies at the Autonomous University of Barcelona in Spain. I also spent some time with four postdocs, two at the University of Campinas supervised by Prof. Marco A. Teixeira, one at the Autonomous University of Barcelona headed by Prof. Jaume Llibre, and another one at the University of Minnesota, supervised by Richard McGehee. In 2022, I obtained my "Habilitation" (Livre docência, in Portuguese) from the University of Campinas. I am an assistant professor at the Federal University of Goiás, working in the Institute of Mathematics and Statistics, being part of the Dynamical Systems Group, and acting as adjunct coordinator of the Graduate Mathematics Program. I am also a CNPq Research Productivity Fellow – Level 2. Here you can find a short version of my CV:
My primary research interest is concentrated in dynamical systems. My research mainly focused on studying trajectories associated with vector fields, particularly those from non-smooth vector fields or with distinct time scales. My main lines of research are the following:
Singular perturbation theory
Local and global bifurcations and structural stability
Limit cycles and other minimal sets
Limit sets and asymptotic stability
Transitivity and chaos
Applications of non-smooth systems to climate sciences
[ 25 ] Characterization of non-deterministic chaos in two-dimensional non-smooth vector fields, Differential Equations and Dynamical Systems, 2025 - with Pedro Mattos and Régis Varão.
[ 24 ] Dynamics of an intermittent HIV treatment using piecewise smooth vector fields with two switching manifolds, Nonlinear Analysis: Real World Applications, 2025 - with Tiago Carvalho, Jackson Cunha and Marco Florentino
[ 23 ] Global Dynamics of Planar Piecewise Linear Inelastic systems having straight lines as switching manifolds, Nonlinear Analysis: Real World Applications, 2024 - with Yovani Villanueva
[ 22 ] Periodic trajectories in planar discontinuous piecewise linear systems with only centers and with a nonregular switching line, Nonlinearity, 2023 - with Ana Maria Alves.
[ 21 ] On Cyclicity in Discontinuous Piecewise Linear near-Hamiltonian Differential Systems with three Zones having a Saddle in the Central one, Nonlinear Dynamics, 2023 - with Claudio Pessoa, Ronísio Ribeiro, Márcio Gouveia and Douglas Novaes.
[ 20 ] Bifurcation of Piecewise Smooth Manifolds from 3D Center-Type Vector Fields, Qualitative theory of Dynamical Systems, 2023 - with Claudio Buzzi and Ana Mereu,
[ 19 ] Periodic orbits in piecewise Riccati vector fields, Discrete and Continuous Dynamical Systems - Series B, 2023 - with Bruno Freitas
[ 18 ] Limit cycles of generic piecewise vector fields in R^3 separated by either one plane or two parallel planes, Bulletin des Sciences Mathematiques, 2022 - with Jaume Llibre and Yovani Villanueva
[ 17 ] Lower bounds for the number of limit cycles in a generalized Rayleight-Liénard oscillator, Nonlinearity, 2022 - with Jaume Llibre and Durval J Tonon
[ 16 ] There Exist Transitive Piecewise Smooth Vector Fields on S2 but Not Robustly Transitive, Journal of Nonlinear Science, 2022 - with Joaby Jucá and Régis Varão.
[ 15 ] Limit sets of discontinuous vector fields on two-dimensional manifolds, Journal of Nonlinear Science, 2021 - with Joaby Jucá.
[ 14 ] Minimal sets and chaos in planar piecewise smooth vector fields, Electronic Journal of Qualitative Theory of Differential Equations, 2020 - with Tiago de Carvalho.
[ 13 ] On Poincaré-Bendixson Theorem and non-trivial minimal sets in planar nonsmooth vector fields, Publicacions Matematiques, 2018 - with Claudio A. Buzzi and Tiago de Carvalho.
[ 12 ] Poincaré recurrence theorem for non-smooth vector fields, Zeitschrift fur Angewandte Mathematik und Physik, 2017 - with Márcio R. A. Gouveia.
[ 11 ] Birth of limit cycles from a 3D triangular center of a piecewise smooth vector field, IMA Journal of Applied Mathematics, 2017 - with Tiago de Carvalho, Marco A. Teixeira and Durval J. Tonon.
[ 10 ] Zero-Hopf bifurcation in a Chua system, Nonlinear Analysis: Real World Applications, 2017 - with Jaume Llibre.
[ 9 ] Chaotic planar piecewise smooth vector fields with non-trivial minimal sets, Ergodic Theory & Dynamical Systems, 2016 - with Claudio A. Buzzi and Tiago de Carvalho.
[ 8 ] Jump bifurcations in some degenerate planar piecewise linear differential systems with three zones, Physica. D, Nonlinear Phenomena, 2016 - with Rubens Pazim and Enrique Ponce.
[ 7 ] Detecting periodic orbits in some 3D chaotic quadratic polynomial differential systems, Discrete and Continuous Dynamical Systems - Series B, 2016 - with Tiago de Carvalho, Jaume Llibre and Durval J. Tonon.
[ 6 ] Bifurcation of limit cycles from a non-smooth perturbation of a two-dimensional isochronous cylinder, Bulletin des Sciences Mathématiques, 2015 - with Claudio A. Buzzi and Ana C. O. Mereu.
[ 5 ] Sufficient conditions for the existence of periodic Solutions of the extended Duffing-Van der Pol oscillator, International Journal of Computer Mathematics, 2015 - with Jaume Llibre.
[ 4 ] On the number of limit cycles in discontinuous piecewise linear differential systems with two pieces separated by a straight line, Journal of Mathematical Analysis and Applications, 2014 - with Jaume Llibre.
[ 3 ] Periodic solutions of El Niño model through the Vallis differential system, Discrete and Continuous Dynamical Systems - Series A, 2014 - with Jaume Llibre.
[ 2 ] Zero-Hopf bifurcation in the FitzHugh-Nagumo system, Mathematical Methods in the Applied Sciences, 2014 - with Jaume Llibre and Claudio Vidal.
[ 1 ] Discussion on the limit cycles of the Lev Ginzburg equation by M. Bellamy and R.E. Mickens, Journal of Sound and Vibration, 2012 - with Claudio A. Buzzi, Jaume Llibre and Luis Fernando O. Mello.
Asymptotic stability in a nonsmooth slow-fast climate system presenting boundaries, Rodrigo D. Euzébio. To appear in the series book Advances in Nonlinear Dynamics, 2025.
Trajectories at non-regular points in planar discontinuous piecewise linear differential systems with centers and a non-regular switching discontinuity, Rodrigo D. Euzébio, Luiz F. Gonçalves and Vitor E. R. Souza. To appear in the series book Advances in Nonlinear Dynamics, 2025.
Generic one-parameter families of 3-dimensional Filippov Systems - Rodrigo D. Euzébio, Durval J. Tonon and Marco A. Teixeira [revision requested]
Limit cycles of piecewise linear vector fields in R^3 separated by a plane with a multiple eigenvalue - Rodrigo D. Euzébio, Jaume Llibre and Durval J. Tonon [under review]
Limit sets near a cusp-fold singularity in a class of 3D Filippov systems - Rodrigo D. Euzébio and Angie Romero Varão [under review]
Limit cycles of piecewise smooth vector fields formed by rigid systems and linear centers - Rodrigo D. Euzébio, Vitória C. Fernandes, Luiz Fernando Gonçalves and Jaume Llibre [under review]
Inelastic non-smooth vector fields with the sphere as switching manifold - RD Euzébio, RM Martins and Y Villanueva [submission soon]
Canard explosion in a planar slow-fast climate system - R Cristiano, RD Euzébio, R McGehee and A Moretti [submission soon]
Discontinuous rotated vector fields - AM Alves and RD Euzébio [submission soon]
Bifurcations in a 3D singularly perturbed non-smooth system modeling glacial cycles - RD Euzébio, VC Fernandes and R McGehee
Limit sets in a discontinuous fast–slow climate model - RD Euzébio
Dynamics near nonregular points in planar piecewise linear discontinuous differential systems with centers - RD Euzébio, LF Gonçalves and VER Souza
Doctorate dissertation: Study of minimal sets for discontinuous systems in dimensions 2 and 3
Master dissertation (In Portuguese): The Averaging Methods via Brouwer degree theory and Applications
Research Productivity Scholarship - PQ - CNPq
Coordination: Prof. Dr. Rodrigo Donizete Euzébio
Title: Singularly perturbed discontinuous dynamical systems
Period: 2023 - current
Research supported by: National Council for Scientific and Technological Development [CNPq - grant 308652/2022-3]
UNIVERSAL - CNPq
Coordination: Prof. Dr. Luiz Fernando Gonçalves
Title: Qualitative theory of piecewise smooth vector fields and its applications to biological, climatological, and power converter models
Period: 2025 - current
Research supported by: National Council for Scientific and Technological Development [CNPq - grant 401974/2025-1]
[2023 - 2025] Support for Scientific, Technological and Innovation Research: Scholarships Abroad - CNPq: Discontinuous singularly perturbed dynamical systems: theory and applications [Coordination: Prof. Dr. Rodrigo Donizete Euzébio]
[2017 - 2022] PRONEX - Fapeg/Goiás: Geometry, Singularities and Differential Equations [Coordination: Prof. Dr. Ronaldo Alves Garcia]
[2014 - 2022] PROCAD - Capes: Nonlinear differential equations [Coordination: Prof. Dr. Marco Antônio Teixeira]
[2017 - 2022] UNIVERSAL - CNPq: Topological and ergodic aspects of piecewise smooth dynamical systems [Coordination: Prof. Dr. Rodrigo Donizete Euzébio]
Adimar Moretti Júnior. Thesis' title: Smooth and non-smooth slow-fast systems definidos em variedades com bordo - 2022, Capes [Lattes]
Vitória Chaves Fernandes. Thesis' title: Discontinuous singular perturbed differential systems applied to climate sciences- 2023, Capes. [Lattes]
[Co-supervisor] Vitor Emanoel Resplandes de Souza. Thesis' title: Qualitative aspects of piecewise smooth vector fields, 2023, Capes. [Lattes]
[Co-supervisor] Luan Lima da Silva. Thesis' title: Qualitative analysis of fast-slow vector fields with applications, 2024, Capes. [Lattes]
Lygia Machado Rebouças. Projects' title: Qualitative theory of dynamical systems and applications - 2025-2026, CNPq
Letícia da Silva Nunes. Projects' title: Geometric theory of dynamical systems and applications - 2025-2026
Former student projects
Joaby de Souza Jucá, Limit sets and transitivity of piecewise smooth vector fields in bi-dimensional Riemannian manifolds, 2020.
Ana Maria Alves da Silva, Limit cycles in planar piecewise smooth systems having non-regular switches, time scales or rotated properties, Time Scales or Rotated Properties, 2022.
Angie Tatiana Suárez Romero, Piecewise Smooth Vector Fields: Conley Index and Asymptotic Analysis, 2022.
Yovani Adolfo Villanueva Herrera, Global Dynamics of Inelastic and Center-Type Piecewise Smooth Vector Fields in R^2 and R^3, 2022.
Ana Maria Alves da Silva, Minimal sets in planar piecewise linear smooth systems, 2017.
Vitória Chaves Fernandes, Sistemas descontínuos lento-rápidos e aplicações, 2023.
Klayver Henrigle Pricinote Santos Rodrigues, Minimal sets of dynamical systems, 2023.
Victor Gabriel Rodrigues Ribeiro, Introduction to the geometry theory of dynamical systems. 2023.
Klayver Henrigle Pricinote Santos Rodrigues, Introduction to the qualitative theory of dynamical systems [PIBIC], 2022.
Caio Augusto Santos Magalhães, Aspects of qualitative theory of the dynamical systems [PIBIC], 2021.
Caio Augusto Santos Magalhães, Topics of linear algebra and ordinary differential equations [PIBIC], 2020.
Caio Augusto Santos Magalhães, Topics of linear algebra and ordinary differential equations [PROCAD], 2019.
Paulo Henrique Brasil Ribeiro, Limit cycles in piecewise smooth systems [PIBIC], 2018.
Karina Alves Bomtempo, Introduction to the qualitative theory of dynamical systems [PIBIC], 2018.
Robson Luiz Fortuna Filho, Introduction to the bifurcation theory in dynamical systems, 2016.
Elieudes Junior Dering de Lima Silva, Introduction to the bifurcation theory in dynamical systems, 2016.
Pronouns: He / Him / His
Seminars
Directions to the Institute of Mathematics and Statistics