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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 (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)
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, . (16/11471-2, 12/18780-0, 13/21078-8, 12/23591-1)
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, . (16/11471-2)
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, . (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, . (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, . (16/11471-2, 15/24841-0, 15/02517-6)
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, . (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, . (15/02517-6, 16/11471-2, 16/05384-0, 15/02731-8)
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., . (16/11471-2)

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