List of Publications

• L. F. Gonçalves, B. R. Freitas, and R. A. Garcia. Limit cycles in a class of piecewise polynomial differential systems having the unit circle as their switching manifold. Nonlinear Analysis: Real World Applications, v. 91, 104521, 2026. https://doi.org/10.1016/j.nonrwa.2025.104521

• L. F. Gonçalves, A. C. T. Sánchez, and D. J. Tonon. Limit cycles on rigid piecewise smooth dynamical systems governed by even polynomials. Nonlinear Analysis: Real World Applications, v. 91, 104581, 2026. https://doi.org/10.1016/j.nonrwa.2025.104581

• L. F. Gonçalves, R. M. Martins, T. Carvalho, and D. J. Tonon. Completely Integrable Three Dimensional Linear Differential Systems and the Creation of Limit Cycles. Matemática Contemporânea, 2026. https://doi.org/10.1007/s44425-026-00052-9

• L. F. Gonçalves, R. D. Euzébio, V. C. Fernandes, and J. Llibre. Limit Cycles of Piecewise Smooth Vector Fields Formed by Rigid Systems and Linear Centers. Journal of Nonlinear Science, v. 36, 88, 2026. https://doi.org/10.1007/s00332-026-10308-1

• L. F. Gonçalves and R. A. Garcia. Bifurcation of limit cycles in the coupling of two van der Pol type oscillators. Chaos, Solitons & Fractals, v. 211, 118881, 2026. https://doi.org/10.1016/j.chaos.2026.118881

• L. F. Gonçalves and R. A. Garcia. Distance-Induced Vector Fields Associated to Triangles. Qualitative Theory of Dynamical Systems, v. 25, 175, 2026. https://doi.org/10.1007/s12346-026-01600-2

• T. Carvalho, L. F. Gonçalves, and B. R. Freitas. Singularly perturbed Hopf boundary equilibrium of planar piecewise smooth vector fields. Journal of Differential Equations, v. 440, 113454, 2025. https://doi.org/10.1016/j.jde.2025.113454

• T. Carvalho, L. F. Gonçalves, and B. R. Freitas. Geometric singular perturbation on a positive measure minimal set of a planar piecewise smooth vector field. Nonlinear Analysis: Hybrid Systems, v. 58, 101628, 2025. https://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, v. 113, 2024. https://doi.org/10.1007/s11071-024-10615-w

• T. Carvalho, L. F. Gonçalves, and J. Llibre. On the Limit Cycles of a Class of Discontinuous Piecewise Differential Systems Formed by Two Rigid Centers Governed by Odd Degree Polynomials. International Journal of Bifurcation and Chaos, v. 32, n. 16, 2250245, 2022. https://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, v. 31, n. 15, 2150224, 2021. https://doi.org/10.1142/S0218127421502242

• D. C. Braga, A. F. Fonseca, L. F. Gonçalves, and L. F. Mello. Limit Cycles Bifurcating from an Invisible Fold–Fold in Planar Piecewise Hamiltonian Systems. Journal of Dynamical and Control Systems, v. 27, pp. 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, pp. 4263–4280, 2021. https://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, 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, pp. 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, pp. 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, 125179, 2020. https://doi.org/10.1016/j.amc.2020.125179

• D. C. Braga, A. 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, 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, 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, pp. 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. Journal of Dynamical and Control Systems, v. 26, pp. 233–242, 2019. https://doi.org/10.1007/s10883-019-09446-5

• PhD Thesis 

• Master thesis 

Conference Proceedings

• R. D. Euzébio, L. F. Gonçalves, and V. E. R. Souza. Trajectories at Non-regular Points in Planar Discontinuous Piecewise Linear Differential Systems with Centers and Non-regular Switching Discontinuity. Proceedings of the Fourth International Nonlinear Dynamics Conference (NODYCON 2025), Springer Nature Switzerland, v. 1, pp. 405–415, 2026.

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!