Rodrigo Donizete Euzébio

Happening now...

I am coordinating and co-organizing the following events:

Research and Publications

Research interests

My primary research interest is concentrated in dynamical systems. My research mainly concentrates on studying trajectories associated with vector fields, particularly those coming from non-smooth vector fields. My main lines of research are the following:

• Transitivity and non-deterministic chaos

• The existence of limit cycles and other minimal sets

• Local and global bifurcations and structural stability

• Limit sets and asymptotic stability

• Singular perturbation theory

• Applications of non-smooth systems to climate sciences
  
  

Recently, I have been more and more interested in fast-slow systems and applications of non-smooth systems to real problems such as climate sciences. I have just started some collaborations and student supervision on those matters.

Publications list

[ 23 ] Periodic trajectories in planar discontinuous piecewise linear systems with only centers and with a nonregular switching line, Nonlinearity, 2023 -  with Ana Maria Alves.

[ 22 ] 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.

[ 21 ] Global Dynamics of Planar Piecewise Linear Inelastic systems having straight lines as switching manifolds, Nonlinear Analysis: Real World Applications, 2023 -  with Yovani Villanueva

[ 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.

Submitted manuscripts

• Limit sets near a cusp-fold singularity in a class of 3D Filippov systems - Rodrigo D. Euzébio and Angie Romero Varão  [under review]

• Topological transitivity implies chaos for two-dimensional Filippov systems - Rodrigo D. Euzébio and Régis Varão  [under review]  [ArXiv]

• Dynamics of an intermittent HIV treatment using piecewise smooth vector fields with two switching manifolds - Tiago de Carvalho,  Jackson Cunha, Rodrigo D. Euzébio and Marco Florentino [under review]

Coming soon

• Discontinuous rotated vector fields - AM Alves and RD Euzébio [submission soon]

• Inelastic non-smooth vector fields with the sphere as switching manifold -  RD Euzébio, RM Martins and Y Villanueva [submission soon]

• Co-dimension one Fillipov systems on R^3 - RD Euzébio, MA Teixeira and DJ Tonon

• A new upper bound for the number of limit cycles in discontinuous linear 3D vector fields - CA Buzzi, RD Euzébio and LAF Roberto

• Inelastic planar piecewise linear systems separated by non-degenerate conics - RD Euzébio and Y Villanueva

Others publications

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

Teaching

Linear Algebra [September 2023 - February 2024]