Sliding motion in discontinuous dynamical systems: periodic solutions, homoclinic connections, and nonlinear sliding modes

• Grant number: 16/11471-2
• Support Opportunities: Regular Research Grants
• Start date: September 01, 2016
• End date: August 31, 2018
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Douglas Duarte Novaes
• Grantee: Douglas Duarte Novaes
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

This project aims to develop research in the field of nonsmooth differential equations. We are particularly interested in the sliding dynamics defined on the manifold of discontinuity. At a first moment, using the ideas from Melnikov, we study the bifurcation of a typical cycle of the Filippov systems. We also study the robustness of the chaotic behavior existing nearby a sliding Shilnikov orbit. We also track 1-parameters family of smooth vector fields approaching continuously to the discontinuous one and admitting an ordinary Shilnikov connection. Finally we consider the nonlinear sliding modes in discontinuous systems having the set of discontinuity as being algebraic varieties. (AU)

Scientific publications

(8)

(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)

DA CRUZ, LEONARDO P. C.; NOVAES, DOUGLAS D.; TORREGROSA, JOAN. New lower bound for the Hilbert number in piecewise quadratic differential systems. Journal of Differential Equations, v. 266, n. 7, p. 4170-4203, MAR 15 2019. (16/11471-2)

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. (16/11471-2, 12/18780-0, 13/21078-8, 12/23591-1)

BASTOS, JEFFERSON L. R.; BUZZI, CLAUDIO A.; LLIBRE, JAUME; NOVAES, DOUGLAS D.. Melnikov analysis in nonsmooth differential systems with nonlinear switching manifold. Journal of Differential Equations, v. 267, n. 6, p. 3748-3767, SEP 5 2019. (16/11471-2, 18/16430-8, 13/24541-0)

NOVAES, DOUGLAS D.; PONCE, GABRIEL; VARAO, REGIS. Chaos Induced by Sliding Phenomena in Filippov Systems. Journal of Dynamics and Differential Equations, v. 29, n. 4, p. 1569-1583, DEC 2017. (15/02517-6, 16/11471-2, 16/05384-0, 15/02731-8)

LLIBRE, JAUME; NOVAES, DOUGLAS D.; RODRIGUES, CAMILA A. B.. Averaging theory at any order for computing limit cycles of discontinuous piecewise differential systems with many zones. PHYSICA D-NONLINEAR PHENOMENA, v. 353, p. 1-10, SEP 1 2017. (15/02517-6, 16/11471-2, 15/24841-0)

CANDIDO, MURILO R.; LLIBRE, JAUME; NOVAES, DOUGLAS D.. Persistence of periodic solutions for higher order perturbed differential systems via Lyapunov-Schmidt reduction. Nonlinearity, v. 30, n. 9, p. 3560-3586, SEP 2017. (16/11471-2)

NOVAES, DOUGLAS D.; TORREGROSA, JOAN. On extended Chebyshev systems with positive accuracy. Journal of Mathematical Analysis and Applications, v. 448, n. 1, p. 171-186, APR 1 2017. (16/11471-2, 15/24841-0, 15/02517-6)

DA SILVA, P. R.; MEZA-SARMIENTO, I. S.; NOVAES, D. D.. Nonlinear Sliding of Discontinuous Vector Fields and Singular Perturbation. DIFFERENTIAL EQUATIONS AND DYNAMICAL SYSTEMS, v. 30, n. 3, p. 19-pg., 2022-07-01. (16/11471-2)