Study of Polycycles with applications in Game Theory.

• Grant number: 22/14353-1
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate
• Start date: September 01, 2023
• End date: August 31, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Claudio Aguinaldo Buzzi
• Grantee: Paulo Henrique Reis Santana
• Supervisor: Armengol Gasull
• 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
• Institution abroad: Universitat Autònoma de Barcelona (UAB), Spain
• Associated to the scholarship: 21/01799-9 - The Study of vector fields with applications at Game Theory., BP.DR

Abstract

Our main goal is to study the polycycles (also known as graphs) of vector fields with two vertical invariant straight lines and two horizontal invariant straight lines. Such family of vector fields is closely linked with Game Theory. More precisely, we aim to study the existence, genericity, stability, cyclicity and bifurcation diagrams of such polycycles.

Scientific publications

(7)

(The scientific publications listed on this page originate from the Web of Science or SciELO databases. Their authors have cited FAPESP grant or fellowship project numbers awarded to Principal Investigators or Fellowship Recipients, whether or not they are among the authors. This information is collected automatically and retrieved directly from those bibliometric databases.)

SANTANA, PAULO. A note on the stability of periodic orbits of planar Lotka-Volterra systems. Electronic Journal of Qualitative Theory of Differential Equations, v. N/A, n. 35, p. 14-pg., 2025-01-01. (21/01799-9, 19/10269-3, 22/14353-1)

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)

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; 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)

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)

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)