Bifurcation theory of limit cycles by higher order Melnikov functions and applications

DOI10.1016/J.JDE.2024.04.036MaRDI QIDQ6559409

Shanshan Liu, Maoan Han

Publication date: 21 June 2024

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

zbMATH Keywords

limit cycleHopf bifurcationhomoclinic bifurcationhigher order Melnikov function

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 of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

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