Melnikov analysis in a cubic system with a multiple line of critical points

DOI10.1016/j.aml.2023.108787zbMath1527.34057OpenAlexW4384161815MaRDI QIDQ6170097

Jiang Yu, Peixing Yang

Publication date: 15 August 2023

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2023.108787

zbMATH Keywords

limit cyclesMelnikov functions

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) Perturbations, asymptotics of solutions to ordinary differential equations (34E10)

Cites Work

• Limit cycles appearing from the perturbation of a system with a multiple line of critical points
• The third order Melnikov function of a quadratic center under quadratic perturbations
• On the cubic perturbations of the symmetric 8-loop Hamiltonian
• The number of limit cycles from a cubic center by the Melnikov function of any order
• GLOBAL BIFURCATION OF LIMIT CYCLES IN A FAMILY OF MULTIPARAMETER SYSTEM
• On Second Order Bifurcations of Limit Cycles
• Successive derivatives of a first return map, application to the study of quadratic vector fields
• The Number of Limit Cycles for a Class of Cubic Systems with Multiple Parameters

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