The study of vector fields with applications at game theory

• Grant number: 21/01799-9
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: September 01, 2021
• End date: September 21, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Claudio Aguinaldo Buzzi
• Grantee: Paulo Henrique Reis Santana
• Host Institution: Instituto de Biociências, Letras e Ciências Exatas (IBILCE). Universidade Estadual Paulista (UNESP). Campus de São José do Rio Preto. São José do Rio Preto , SP, Brazil
• Associated research grant: 19/10269-3 - Ergodic and qualitative theories of dynamical systems II, AP.TEM
• Associated scholarship(s): 22/14353-1 - Study of polycycles with applications in game theory, BE.EP.DR

Abstract

The goal of the project is the study of planar vector fields with four invariant straight lines, two verticals and two horizontals, aiming its applications on game theory. The objective is to study the phase portraits, the bifurcation diagrans, the integrability of the system, the number of limit cycles, the algebricity and the hyperbolicity of the limit cycles and the annular periods of the planar polynomial vectors fields with these four invariant straight lines. (AU)

Scientific publications

(10)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

SANTANA, PAULO. Stability and Cyclicity of Polycycles in Non-smooth Planar Vector Fields. Qualitative Theory of Dynamical Systems, v. 22, n. 4, p. 33-pg., 2023-12-01. (19/10269-3, 21/01799-9)

BASTOS, JEFFERSON; BUZZI, CLAUDIO; SANTANA, PAULO. On structural stability of evolutionary stable strategies. Journal of Differential Equations, v. 389, p. 38-pg., 2024-01-24. (21/01799-9, 19/10269-3)

BUZZI, CLAUDIO; GASULL, ARMENGOL; SANTANA, PAULO. On the cyclicity of hyperbolic polycycles. Journal of Differential Equations, v. 429, p. 32-pg., 2025-02-25. (19/10269-3, 23/02959-5, 22/14353-1, 21/01799-9)

GASULL, ARMENGOL; SANTANA, PAULO. On a variant of Hilbert's 16th problem. Nonlinearity, v. 37, n. 12, p. 15-pg., 2024-12-02. (22/14353-1, 21/01799-9, 19/10269-3)

BELATTAR, MERYEM; CHEURFA, RACHID; BENDJEDDOU, AHMED; SANTANA, PAULO. An Exactly Solvable Planar Differential System Of Degree Six With An Explicit Algebraic Limit Cycle. APPLIED MATHEMATICS E-NOTES, v. 24, p. 12-pg., 2024-01-01. (19/10269-3, 21/01799-9)

BELATTAR, MERYEM; CHEURFA, RACHID; BENDJEDDOU, AHMED; SANTANA, PAULO. A class of nonlinear oscillators with non-autonomous first integrals and algebraic limit cycles. Electronic Journal of Qualitative Theory of Differential Equations, v. N/A, n. 50, p. 13-pg., 2023-01-01. (21/01799-9, 19/10269-3)

GASULL, ARMENGOL; GOUVEIA, LUIZ F. S.; SANTANA, PAULO. On the limit cycles of a quartic model for Evolutionary Stable Strategies. NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, v. 84, p. 17-pg., 2025-01-06. (22/14353-1, 20/04717-0, 19/10269-3, 22/03801-3, 21/01799-9)

LLIBRE, JAUME; SANTANA, PAULO. Limit cycles and chaos in planar hybrid systems. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, v. 140, p. 13-pg., 2024-10-09. (22/14353-1, 21/01799-9, 19/10269-3)

GASULL, ARMENGOL; SANTANA, PAULO. A NOTE ON HILBERT 16TH PROBLEM. Proceedings of the American Mathematical Society, v. 153, n. 2, p. 9-pg., 2024-12-17. (22/14353-1, 19/10269-3, 21/01799-9)

SANTANA, PAULO. On the structural instability of non-hyperbolic limit cycles on planar polynomial vector fields. SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES, v. N/A, p. 14-pg., 2024-05-20. (22/14353-1, 21/01799-9, 19/10269-3)