List of Publications

• T. Carvalho; L. F. Gonçalves, and Bruno Freitas.  Singularly perturbed Hopf boundary equilibrium of planar piecewise smooth vector fields . JOURNAL OF DIFFERENTIAL EQUATIONS, v. 440, p. 113454-1-32, 2025. http://dx.doi.org/10.1016/j.jde.2025.113454

• T. Carvalho; L. F. Gonçalves, and Bruno Freitas. Geometric singular perturbation on a positive measure minimal set of a planar piecewise smooth vector field . Nonlinear Analysis-Hybrid Systems, v. 58, p. 101628, 2025. http://dx.doi.org/10.1016/j.nahs.2025.101628

• L. F. Gonçalves, D. J. Tonon and M. A. Teixeira.  Generic singularities of relay systems. Nonlinear Dynamics. Vol. 113, (2024). http://dx.doi.org/10.1007/s11071-024-10615-w 

• T. Carvalho; L. F. Gonçalves, and J. Llibre.  On the limit cycles of a class of discontinous piecewise differential systems formed by two rigid centers governed by odd degree polynomials. International Journal of Bifurcation and Chaos. Vol. 32, No. 16, 2250245 (2022). https:///dx.doi.org/10.1142/S0218127422502455 

• T. Carvalho; L. F. Gonçalves , and J. Llibre. Limit cycles on piecewise smooth vector fields with coupled rigid centers. International Journal of Bifurcation and Chaos. Vol. 31, No. 15, 2150224 (2021). https://doi.org/10.1142/S0218127421502242

• Denis C. Braga; Alexander F. Fonseca, L. F. Mello, and L. F. Gonçalves. Limit Cycles Bifurcating from an Invisible Fold–Fold in Planar Piecewise Hamiltonian Systems. J Dyn Control Syst, 27, 179–204 (2021). https://doi.org/10.1007/s10883-020-09478-2 

• T. Carvalho and L. F. Gonçalves. A flow on S2 presenting the ball as its minimal set. Discrete & Continuous Dynamical Systems - B, v. 26, p. 4263-4280, 2021. http://dx.doi.org/10.3934/dcdsb.2020287

• T. Carvalho and L. F. Gonçalves.  Creation of Limit Cycles in Piecewise Smooth Vector Fields Tangent to Nested Tori. Qualitative Theory of Dynamical Systems, v. 20, p. 55, 2021. https://doi.org/10.1007/s12346-021-00491-9

• T. Carvalho, D. D. Novaes and L. F. Gonçalves. Sliding Shilnikov connection in Filippov-type predator-prey model. Nonlinear Dynamics, v. 100, p. 2973-2987, 2020.  https://doi.org/10.1007/s11071-020-05672-w

• T. Carvalho, R. Cristiano, L. F. Gonçalves, and D. J. Tonon. Global analysis of the dynamics of a mathematical model to intermittent HIV treatment. Nonlinear Dynamics, v. 101, p. 719-739, 2020.  https://doi.org/10.1007/s11071-020-05775-4

• D. C. Vicentin, P. F. A Mancera, T. Carvalho, and L. F. Gonçalves. Mathematical model of an antiretroviral therapy to HIV via Filippov theory. Applied Mathematics and Computation, v. 387, p. 125179, 2020.  https://doi.org/10.1016/j.amc.2020.125179

• Denis C. Braga; Alexander F. Fonseca, L. F. Gonçalves, and L. F.Mello. Lyapunov coefficients for an invisible fold-fold singularity in planar piecewise Hamiltonian systems. Journal of Mathematical Analysis and Applications, v. 484, p. 123692, 2020. https://doi.org/10.1016/j.jmaa.2019.123692

• D. S. Rodrigues, P. F. A Mancera, T. Carvalho, and L. F. Gonçalves. Sliding mode control in a mathematical model to chemoimmunotherapy: The occurrence of typical singularities. Applied Mathematics and Computation, v. 387, p. 124782, 2020. https://doi.org/10.1016/j.amc.2019.124782

• D. S. Rodrigues, P. F. A Mancera, T. Carvalho, and L. F. Gonçalves. A mathematical model for chemoimmunotherapy of chronic lymphocytic leukemia. Applied Mathematics and Computation, v. 349, p. 118-133, 2019. https://doi.org/10.1016/j.amc.2018.12.008

• T. Carvalho and L. F. Gonçalves. Combing the Hairy Ball Using a Vector Field Without Equilibria. J Dyn Control Syst, v. 26, p. 233-242, 2019. https://doi.org/10.1007/s10883-019-09446-5

• PhD Thesis 

• Master thesis 

Preprints

• L. F. Gonçalves, T. Carvalho, R. M. Martins, and D. J. Tonon. Classification of completely integrable three dimensional linear differential systems, submitted.

• L. F. Gonçalves, Angela C. T. Sanchez, and D. J. Tonon. Bifurcations of limit cycles for rigid centers on piecewise smooth dynamical systems, submitted.

If you have any interest in collaborations, please do not hesitate to let me know. Feel free to contact me!

New collaborators are always welcome!