Limit cycles of a class of Liénard systems with restoring forces of seventh degree

DOI10.1016/j.amc.2017.08.008zbMath1426.34041OpenAlexW2752191922MaRDI QIDQ1740268

Junmin Yang, Wei Ding

Publication date: 29 April 2019

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2017.08.008

zbMATH Keywords

Liénard systembifurcationlimit cyclecuspidal loop16th Hilbert problem

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)

Related Items (2)

On the Number of Limit Cycles Bifurcating from a Compound Polycycle ⋮ ON THE NUMBER OF LIMIT CYCLES FOR A QUINTIC LIÉNARD SYSTEM UNDER POLYNOMIAL PERTURBATIONS

Cites Work

• Unnamed Item
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• Small-amplitude limit cycles of polynomial Liénard systems
• Limit cycles of some polynomial Liénard systems
• Multiple limit cycles of some strongly nonlinear Liénard-van der Pol oscillator
• Limit cycles in a Liénard system with a cusp and a nilpotent saddle of order 7
• Bifurcation of limit cycles by perturbing a class of hyper-elliptic Hamiltonian systems of degree five
• Limit cycles in generalized Liénard systems
• Limit cycles near homoclinic and heteroclinic loops
• Estimating the number of limit cycles in polynomial systems
• On Hopf cyclicity of planar systems
• Mathematical problems for the next century
• Perturbation from an elliptic Hamiltonian of degree four. IV: Figure eight-loop.
• New lower bounds for the Hilbert number of polynomial systems of Liénard type
• Limit cycle bifurcations of some Liénard systems
• Limit cycle bifurcations by perturbing a cuspidal loop in a Hamiltonian system
• THE NUMBER OF LIMIT CYCLES IN A Z₂-EQUIVARIANT LIÉNARD SYSTEM
• The number of small-amplitude limit cycles of Liénard equations
• Limit cycles of the generalized polynomial Liénard differential equations
• Small-amplitude limit cycles of certain Liénard systems
• Small-amplitude limit cycle bifurcations for Liénard systems with quadratic or cubic damping or restoring forces
• HOPF BIFURCATIONS FOR NEAR-HAMILTONIAN SYSTEMS
• Bifurcation of Limit Cycles for Some Liénard Systems with a Nilpotent Singular Point

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