Special cubic perturbations of the Duffing oscillator \(x=x-x^3\) near the eight-loop
DOI10.1007/s00009-021-01868-5OpenAlexW3199719609MaRDI QIDQ2238747
Ameni Gargouri, Bassem Ben Hamed, Lyubomir Gavrilov
Publication date: 2 November 2021
Published in: Mediterranean Journal of Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1907.00669
Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Perturbations of ordinary differential equations (34D10) 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)
Cites Work
- Perturbations of symmetric elliptic Hamiltonians of degree four in a complex domain
- On the number of limit cycles which appear by perturbation of two-saddle cycles of planar vector fields
- Perturbations of symmetric elliptic Hamiltonians of degree four
- Applications of centre manifold theory
- Higher order bifurcations of limit cycles
- Bifurcation of planar vector fields and Hilbert's sixteenth problem
- Alien limit cycles near a Hamiltonian 2-saddle cycle
- Perturbation from an elliptic Hamiltonian of degree four. IV: Figure eight-loop.
- Perturbations of quadratic Hamiltonian two-saddle cycles
- On the number of limit cycles which appear by perturbation of Hamiltonian two-saddle cycles of planar vector fields
- Limit cycle bifurcations near a 2-polycycle or double 2-polycycle of planar systems
- Cyclicity of period annuli and principalization of Bautin ideals
- Finite cyclicity of nontrivial double loops
- On Second Order Bifurcations of Limit Cycles
- Hilbert’s 16th problem on a period annulus and Nash space of arcs
- Abelian integrals and limit cycles
- Unnamed Item
- Unnamed Item
This page was built for publication: Special cubic perturbations of the Duffing oscillator \(x=x-x^3\) near the eight-loop
