THE NUMBER OF LIMIT CYCLES IN A Z2-EQUIVARIANT LIÉNARD SYSTEM

DOI10.1142/S0218127413500855zbMath1270.34054OpenAlexW1612296483MaRDI QIDQ2845301

Hui Zhong, Yanqin Xiong

Publication date: 22 August 2013

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218127413500855

zbMATH Keywords

Hopf bifurcationMelnikov functionhomoclinic loopheteroclinic loop\(Z_2\)-equivariant compound cycle

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Symmetries, invariants of ordinary differential equations (34C14) 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) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (8)

Simultaneity of centres in ℤ _q -equivariant systems ⋮ Hopf Bifurcation of Z2-Equivariant Generalized Liénard Systems ⋮ A Quintic \(\boldsymbol{\mathbb{Z}_2}\)-Equivariant Liénard System Arising from the Complex Ginzburg–Landau Equation ⋮ Limit cycle bifurcations in a class of quintic \(Z_2\)-equivariant polynomial systems ⋮ Bifurcations of limit cycles in equivariant quintic planar vector fields ⋮ Limit cycles of a class of Liénard systems with restoring forces of seventh degree ⋮ New lower bounds for the Hilbert number of polynomial systems of Liénard type ⋮ LIMIT CYCLE BIFURCATIONS IN DISCONTINUOUS PLANAR SYSTEMS WITH MULTIPLE LINES

Cites Work

• The number of small-amplitude limit cycles of Liénard equations
• Polynomial systems: a lower bound for the Hilbert numbers

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