Melnikov functions and limit cycles in piecewise smooth perturbations of a linear center using regularization method

DOI10.1016/j.nonrwa.2017.01.003zbMath1393.34030OpenAlexW2581971491MaRDI QIDQ518728

Denis de Carvalho Braga, Luis Fernando Mello, Alexander Fernandes da Fonseca

Publication date: 30 March 2017

Published in: Nonlinear Analysis. Real World Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.nonrwa.2017.01.003

zbMATH Keywords

limit cycleperiodic orbitMelnikov functionregularization methodpiecewise smooth 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) Discontinuous ordinary differential equations (34A36) Perturbations, asymptotics of solutions to ordinary differential equations (34E10)

Related Items (4)

Bifurcation of limit cycles from a parabolic-parabolic type critical point in a class of planar piecewise smooth quadratic systems ⋮ On the number of limit cycles of planar piecewise smooth quadratic systems with focus-parabolic type critical point ⋮ Bifurcation of Periodic Orbits Crossing Switching Manifolds Multiple Times in Planar Piecewise Smooth Systems ⋮ Limit Cycles of Planar Piecewise Smooth Quadratic Systems with Focus-Parabolic Type Critical Points

Cites Work

• Structurally stable discontinuous vector fields in the plane.
• Limit cycles in discontinuous classical Liénard equations
• Equivalence of the Melnikov function method and the averaging method
• LOWER BOUNDS FOR THE MAXIMUM NUMBER OF LIMIT CYCLES OF DISCONTINUOUS PIECEWISE LINEAR DIFFERENTIAL SYSTEMS WITH A STRAIGHT LINE OF SEPARATION
• A NOTE ON A PIECEWISE-LINEAR DUFFING-TYPE SYSTEM
• BIFURCATION OF LIMIT CYCLES BY PERTURBING PIECEWISE HAMILTONIAN SYSTEMS
• Ordinary Differential Equations with Applications
• ON THE NUMBER OF LIMIT CYCLES IN PIECEWISE-LINEAR LIÉNARD SYSTEMS
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Melnikov functions and limit cycles in piecewise smooth perturbations of a linear center using regularization method