A new cubic system having eleven limit cycles

DOI10.3934/dcds.2005.12.675zbMath1085.34027OpenAlexW2034022724MaRDI QIDQ1779046

Ping Bi, Yu-Hai Wu, Mao'an Han

Publication date: 21 June 2005

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2005.12.675

zbMATH Keywords

stabilitycubic systemlimit cyclehomoclinic loopsaddle connection16th Hilbert's problem

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Population dynamics (general) (92D25) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07)

Related Items (15)

On the number of limit cycles of a \(\mathbb{Z}_4\)-equivariant quintic near-Hamiltonian system ⋮ On the Number of Limit Cycles by Perturbing a Piecewise Smooth Liénard Model ⋮ Center and isochronous center conditions for switching systems associated with elementary singular points ⋮ Heteroclinic loop bifurcations by perturbing a class of \(\mathrm{Z}_2\)-equivariant quadratic switching Hamiltonian systems with nilpotent singular points ⋮ Melnikov function and limit cycle bifurcation from a nilpotent center ⋮ Lower bounds for the Hilbert number of polynomial systems ⋮ On the limit cycles of a quintic planar vector field ⋮ ASYMPTOTIC EXPANSIONS OF MELNIKOV FUNCTIONS AND LIMIT CYCLE BIFURCATIONS ⋮ New configurations of 24 limit cycles in a quintic system ⋮ Bifurcations of limit cycles in a \(Z_{4}\)-equivariant quintic planar vector field ⋮ Symbolic computation of limit cycles associated with Hilbert's 16th problem ⋮ Bifurcations of the limit cycles in a \(z_3\)-equivariant quartic planar vector field ⋮ Poincaré bifurcation of limit cycles from a Liénard system with a homoclinic loop passing through a nilpotent saddle ⋮ ON THE NUMBER AND DISTRIBUTIONS OF LIMIT CYCLES OF A PLANAR QUARTIC VECTOR FIELD ⋮ On the Limit Cycles of a Perturbed Z₃-Equivariant Planar Quintic Vector Field

This page was built for publication: A new cubic system having eleven limit cycles