Periodic solutions dor discontinuous dynamical systems with symmetry

• Grant number: 13/21078-8
• Support type: Scholarships abroad - Research Internship - Post-doctor
• Effective date (Start): January 01, 2014
• Effective date (End): June 30, 2014
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal researcher: Marco Antônio Teixeira
• Grantee: Iris de Oliveira Zeli
• Supervisor abroad: Jaume Llibre
• Home Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Research place: Universitat Autònoma de Barcelona (UAB), Spain
• Associated to the scholarship: 12/23591-1 - Singularities theory on dynamical systems in presence of symmetry, BP.PD

Abstract

The study of the periodic solutions for planar continuous piecewise linear systems, when they have only two linearity regions separated by a straight line is the simplest possible configuration in piecewise linear systems. We remark that even in this seemingly simple case, only after a thorough analysis it was possible to establish the existence at most of one limit cycle for such systems. The reason for that misleading simplicity of piecewise linear systems is twofold. First, even one can easily integrate solutions in any linearity region, the time that each orbit requires to pass from a linearity region to each other is unknown and so the matching of the corresponding solutions is an intricate problem. Second, the number of parameters to consider in order to be sure that one copes with all possible configurations is typically not small, so that the achievement of efficient canonical forms with fewer parameters is crucial.Our our goal is the study of the periodic solutions of the discontinuous piecewise linear systems in $\R^3$, since there are very few results in that direction. But in a first approach to this problem we shall restrict our attention to the reversible linear systems. More precisely, the objective of our project is to start in a systematic way the study of the periodic solutions of the reversible discontinuous piecewise linear systems having two zones of linearity. (AU)

Scientific publications

(4)

(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)

LLIBRE, JAUME; NOVAES, DOUGLAS D.; ZELI, IRIS O. Limit cycles of piecewise polynomial perturbations of higher dimensional linear differential systems. REVISTA MATEMATICA IBEROAMERICANA, v. 36, n. 1, p. 291-318, 2020. Web of Science Citations: 1.

NOVAES, DOUGLAS D.; SEARA, TERE M.; TEIXEIRA, MARCO A.; ZELI, IRIS O. Study of Periodic Orbits in Periodic Perturbations of Planar Reversible Filippov Systems Having a Twofold Cycle. SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, v. 19, n. 2, p. 1343-1371, 2020. Web of Science Citations: 0.

NOVAES, DOUGLAS D.; TEIXEIRA, MARCO A.; ZELI, IRIS O. The generic unfolding of a codimension-two connection to a two-fold singularity of planar Filippov systems. Nonlinearity, v. 31, n. 5, p. 2083-2104, MAY 2018. Web of Science Citations: 1.

LLIBRE, JAUME; TEIXEIRA, MARCO A.; ZELI, IRIS O. Birth of limit cycles for a class of continuous and discontinuous differential systems in (d+2)-dimension. DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL, v. 31, n. 3, p. 237-250, SEP 2016. Web of Science Citations: 2.