Bifurcation of limit cycles near polycycles with \(n\) vertices

DOI10.1016/j.chaos.2004.02.031zbMath1060.37040OpenAlexW2006882704MaRDI QIDQ1766639

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

Publication date: 8 March 2005

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.chaos.2004.02.031

zbMATH Keywords

perturbationssaddle pointsHilbert's 16th problemseparatrix

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) 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) Hyperbolic singular points with homoclinic trajectories in dynamical systems (37G20)

Related Items (13)

Stability and cyclicity of polycycles in non-smooth planar vector fields ⋮ Limit cycle bifurcations near a double 2-polycycle on the cylinder ⋮ ON THE NUMBER AND DISTRIBUTIONS OF LIMIT CYCLES IN A QUINTIC PLANAR VECTOR FIELD ⋮ Limit cycle bifurcations by perturbing a class of integrable systems with a polycycle ⋮ On the limit cycles of a quintic planar vector field ⋮ Bifurcations of limit cycles in a perturbed quintic Hamiltonian system with six double homoclinic loops ⋮ Novel frequency-domain criterion for elimination of limit cycles in a class of digital filters with single saturation nonlinearity ⋮ Suppression of limit cycles in second-order companion form digital filters with saturation arithmetic ⋮ Bifurcations of limit cycles in a \(Z_{4}\)-equivariant quintic planar vector field ⋮ On the perturbations of a Hamiltonian system ⋮ EXISTENCE CONDITIONS OF THIRTEEN LIMIT CYCLES IN A CUBIC SYSTEM ⋮ On the limit cycles of a Hamiltonian under \(Z_4\)-equivariant quintic perturbation ⋮ Bifurcations of the limit cycles in a \(z_3\)-equivariant quartic planar vector field

Cites Work

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