Slow divergence integral and its application to classical Liénard equations of degree 5

DOI10.1016/j.jde.2014.08.015zbMath1312.34073OpenAlexW1995382999MaRDI QIDQ462904

Chengzhi Li, Kening Lu

Publication date: 22 October 2014

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

Full work available at URL: https://doi.org/10.1016/j.jde.2014.08.015

zbMATH Keywords

singular perturbationcyclicityslow divergence integralLiénard equation of degree fiveslow-fast cycle

Mathematics Subject Classification ID

Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Singular perturbations for ordinary differential equations (34E15) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08)

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Cites Work

• Unnamed Item
• Classical Liénard equations of degree \(n\geqslant 6\) can have \([\frac{n-1}{2}+2\) limit cycles]
• Cyclicity of common slow-fast cycles
• Uniqueness of limit cycles for Liénard differential equations of degree four
• Geometric singular perturbation theory for ordinary differential equations
• Canard cycle transition at a slow-fast passage through a jump point
• Extending Geometric Singular Perturbation Theory to Nonhyperbolic Points---Fold and Canard Points in Two Dimensions
• Canard solutions at non-generic turning points
• More limit cycles than expected in Liénard equations
• Canard cycles in the presence of slow dynamics with singularities
• Canard cycles and center manifolds
• Multiple canard cycles in generalized Liénard equations
• Relaxation oscillation and canard explosion

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