Bifurcation of limit cycles from a hyper-elliptic Hamiltonian system with a double heteroclinic loops

DOI10.1186/1687-1847-2012-224zbMath1377.34040OpenAlexW2116229684WikidataQ59290123 ScholiaQ59290123MaRDI QIDQ1690886

Xian Bo Sun

Publication date: 12 January 2018

Published in: Advances in Difference Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/1687-1847-2012-224

zbMATH Keywords

Liénard systembifurcationlimit cycleChebyshev systemheteroclinic loops

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) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (6)

Limit cycle bifurcations near a generalized homoclinic loop in piecewise smooth systems with a hyperbolic saddle on a switch line ⋮ Bifurcation of limit cycles from a Liénard system with a heteroclinic loop connecting two nilpotent saddles ⋮ Perturbation of a period annulus bounded by a heteroclinic loop connecting two hyperbolic saddles ⋮ Perturbations of a class of hyper-elliptic Hamiltonian systems of degree seven with nilpotent singular points ⋮ Bounding the number of limit cycles for a polynomial Liénard system by using regular chains ⋮ Perturbation of a period annulus bounded by a saddle-saddle cycle in a hyperelliptic Hamiltonian systems of degree seven

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