Higher order Melnikov analysis for planar piecewise linear vector fields with nonlinear switching curve

DOI10.1016/j.jde.2021.03.039zbMath1466.34023arXiv2006.11352OpenAlexW3036735015MaRDI QIDQ2020204

Oscar A. R. Cespedes, Kamila da S. Andrade, Dayane R. Cruz, Douglas Duarte Novaes

Publication date: 23 April 2021

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2006.11352

zbMATH Keywords

periodic solutionsMelnikov theoryFilippov systemspiecewise linear differential systemsnonlinear switching manifold

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Discontinuous ordinary differential equations (34A36)

Related Items

Limit Cycles of a Class of Discontinuous Piecewise Differential Systems Separated by the Curve y = xn Via Averaging Theory ⋮ The cyclicity of a class of global nilpotent center under perturbations of piecewise smooth polynomials with four zones ⋮ On the number of limit cycles bifurcating from the linear center with an algebraic switching curve ⋮ Non-equivalence between the Melnikov and the averaging methods for nonsmooth differential systems ⋮ The number of limit cycles of a kind of piecewise quadratic systems with switching curve \(y = x^m\) ⋮ Cyclicity of a Class of Hamiltonian Systems under Perturbations of Piecewise Smooth Polynomials ⋮ Some open problems in low dimensional dynamical systems ⋮ On the Hilbert number for piecewise linear vector fields with algebraic discontinuity set ⋮ Limit cycles in piecewise polynomial Hamiltonian systems allowing nonlinear switching boundaries ⋮ On the existence of limit cycles and invariant surfaces for sewing piecewise linear differential systems on \(\mathbb{R}^3\)

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