Melnikov functions of arbitrary order for piecewise smooth differential systems in \(\mathbb{R}^n\) and applications

DOI10.1016/j.jde.2022.01.019zbMath1495.34026OpenAlexW4205903613MaRDI QIDQ2074451

Xingwu Chen, Jaume Llibre, Tao Li

Publication date: 10 February 2022

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

Full work available at URL: https://doi.org/10.1016/j.jde.2022.01.019

zbMATH Keywords

Hilbert's 16th problemMelnikov theorylimit cycle bifurcationpiecewise smooth differential systemfold-fold singularity

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) Averaging method for ordinary differential equations (34C29) 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) Perturbations, asymptotics of solutions to ordinary differential equations (34E10)

Related Items (3)

Impact limit cycles in the planar piecewise linear hybrid systems ⋮ 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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