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


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)

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Scientific publications (7)
(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)
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. Web of Science Citations: 0.
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. Web of Science Citations: 3.
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.
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. Web of Science Citations: 1.
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. Web of Science Citations: 5.
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. Web of Science Citations: 6.
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. Web of Science Citations: 10.

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