Study of crossing limit cycles in piecewise smooth systems on the plane

• Grant number: 22/07822-5
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: February 01, 2023
• End date: December 31, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Alex Carlucci Rezende
• Grantee: Ali Bakhshalizadeh Badaki
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
• Associated research grant: 19/21181-0 - New frontiers in Singularity Theory, AP.TEM

Abstract

We present a criterion that provides an easy sufficient condition in order for a collection of line integrals to have the Chebyshev property. This condition involves the functions in the integrand of the line integrals and can be checked, in many cases, in a purely algebraic way. By using this criterion, the number of limit cycles for discontinuous piecewise differential systems formed by two differential systems separated by a straight line are studied, when these differential systems are Hamiltonians in both sides.

Scientific publications

(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)

BAKHSHALIZADEH, ALI; LLIBRE, JAUME; REZENDE, ALEX C.. Global dynamics analysis of a class of quadratic polynomial differential systems with an invariant plane in R³. NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, v. 32, n. 4, p. 40-pg., 2025-07-01. (22/07822-5)