PERIODIC ORBIT OF THE PENDULUM WITH A SMALL NONLINEAR DAMPING

DOI10.11948/2018.649zbMath1459.34102OpenAlexW2782973843MaRDI QIDQ5147906

Chengzhi Li, Minhua Cheng

Publication date: 29 January 2021

Published in: Journal of Applied Analysis & Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.11948/2018.649

zbMATH Keywords

periodic orbitsbifurcationabelian integralspendulum with a nonlinear damping

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Bifurcation theory for ordinary differential equations (34C23) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Perturbations, asymptotics of solutions to ordinary differential equations (34E10) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08) Nonautonomous smooth dynamical systems (37C60)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Bounding the number of zeros of certain abelian integrals
• Limit cycles of differential equations
• Periodic orbits in 3-dimensional systems and application to a perturbed Volterra system
• Cyclicity 1 and 2 conditions for a 2-polycycle of integrable systems on the plane
• Alien limit cycles near a Hamiltonian 2-saddle cycle
• A criterion for determining the monotonicity of the ratio of two Abelian integrals
• A Chebyshev criterion for Abelian integrals