On the number of limit cycles of a class of Liénard-Rayleigh oscillators

DOI10.1016/j.physd.2022.133366OpenAlexW4281629251MaRDI QIDQ2150434

Zhen Yuan, Ai Ke, Mao'an Han

Publication date: 27 June 2022

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physd.2022.133366

zbMATH Keywords

bifurcationlimit cycleMelnikov functionnear-Hamiltonian system

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) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) (34B30)

Related Items

On the existence and uniqueness of limit cycles for hybrid oscillators ⋮ On the indices of singular points for planar bounded piecewise smooth polynomial vector field

Cites Work

• Unnamed Item
• Unnamed Item
• Creation-annihilation process of limit cycles in the Rayleigh-Duffing oscillator
• Limit cycle bifurcations in a class of near-Hamiltonian systems with multiple parameters
• Hopf and homoclinic bifurcations for near-Hamiltonian systems
• Limit cycles of differential equations
• Loss of stability of self-oscillations close to resonance and versal deformations of equivariant vector fields
• Linear estimate of the number of zeros of Abelian integrals for a kind of quartic Hamiltonians
• Non-existence, existence, and uniqueness of limit cycles for a generalization of the van der Pol-Duffing and the Rayleigh-Duffing oscillators
• Bifurcation of limit cycles of the nongeneric quadratic reversible system with discontinuous perturbations
• Linear estimate for the number of zeros of Abelian integrals with cubic Hamiltonians
• ON THE STUDY OF LIMIT CYCLES OF THE GENERALIZED RAYLEIGH–LIENARD OSCILLATOR
• FURTHER STUDIES ON LIMIT CYCLE BIFURCATIONS FOR PIECEWISE SMOOTH NEAR-HAMILTONIAN SYSTEMS WITH MULTIPLE PARAMETERS<inline-formula><tex-math id="M1">$ ^* $</tex-math></inline-formula>
• HOPF BIFURCATIONS FOR NEAR-HAMILTONIAN SYSTEMS