Up to second order Melnikov functions for general piecewise Hamiltonian systems with nonregular separation line

DOI10.1016/j.jde.2021.03.020zbMath1469.34049OpenAlexW3139176131MaRDI QIDQ2662494

Yuan Yang, Jiang Yu, Peixing Yang

Publication date: 13 April 2021

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

Full work available at URL: https://doi.org/10.1016/j.jde.2021.03.020

zbMATH Keywords

limit cyclesMelnikov functionspiecewise linear system

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) Perturbations, asymptotics of solutions to ordinary differential equations (34E10) Periodic, homoclinic and heteroclinic orbits of finite-dimensional Hamiltonian systems (37J46)

Related Items (7)

Global dynamics of a piecewise smooth system with a fold-cusp and general parameters ⋮ The number of limit cycles of a kind of piecewise quadratic systems with switching curve \(y = x^m\) ⋮ Cyclicity near infinity in piecewise linear vector fields having a nonregular switching line ⋮ Bifurcations of limit cycles in piecewise smooth Hamiltonian system with boundary perturbation ⋮ Limit cycles near a homoclinic loop connecting a tangent saddle in a perturbed quadratic Hamiltonian system ⋮ Bifurcation of limit cycles in a piecewise smooth near-integrable system ⋮ Limit cycle bifurcations by perturbing piecewise Hamiltonian systems with a nonregular switching line via multiple parameters

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