An estimation for the number of limit cycles in a Liénard-like perturbation of a quadratic nonlinear center

DOI10.1007/s11071-014-1655-zzbMath1331.34045OpenAlexW2053260593MaRDI QIDQ494890

Ana Cristina Mereu, Ricardo Miranda Martins, Regilene D. S. Oliveira

Publication date: 2 September 2015

Published in: Nonlinear Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11071-014-1655-z

zbMATH Keywords

isochronous centerbifurcation of limit cyclesaveraging theoryquadratic systems

Mathematics Subject Classification ID

Related Items (1)

Limit cycles for quadratic and cubic planar differential equations under polynomial perturbations of small degree

Cites Work

• Bifurcation of limit cycles in a quintic system with ten parameters
• Limit cycles for generalized Kukles polynomial differential systems
• Classical Liénard equations of degree \(n\geqslant 6\) can have \([\frac{n-1}{2}+2\) limit cycles]
• Normal forms, Melnikov functions and bifurcations of limit cycles
• Uniqueness of limit cycles for Liénard differential equations of degree four
• Bifurcation of limit cycles from quadratic isochrones
• The third order Melnikov function of a quadratic center under quadratic perturbations
• Limit cycles in generalized Liénard systems
• Averaging methods for finding periodic orbits via Brouwer degree.
• Mathematical problems for the next century
• Generalized quadratic Liénard equations
• Generalized cubic Liénard equations
• Limit cycles of generalized Liénard equations
• Limit cycle bifurcations in a class of quintic \(Z_2\)-equivariant polynomial systems
• More limit cycles than expected in Liénard equations
• Limit cycles of the generalized polynomial Liénard differential equations
• Small-amplitude limit cycle bifurcations for Liénard systems with quadratic or cubic damping or restoring forces
• Bifurcation of Limit Cycles from a Non-Hamiltonian Quadratic Integrable System with Homoclinic Loop
• Periodic orbits, invariant tori, and cylinders of Hamiltonian systems near integrable ones having a return map equal to the identity
• LIMIT CYCLES IN HIGHLY NON-LINEAR DIFFERENTIAL EQUATIONS
• Averaging methods in nonlinear dynamical systems
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