ON THE MAXIMUM NUMBER OF LIMIT CYCLES OF A CLASS OF GENERALIZED LIÉNARD DIFFERENTIAL SYSTEMS

DOI10.1142/S0218127412500630zbMath1270.34050MaRDI QIDQ2843554

Jorge L. López-López, Justino Alavez-Ramírez, Jaume Llibre, Gamaliel Blé

Publication date: 23 August 2013

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

zbMATH Keywords

limit cyclespolynomialsLiénard differential systems

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) 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 (7)

Limit cycles of generalized Liénard polynomial differential systems via averaging theory ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Bifurcation of periodic orbits of periodic equations with multiple parameters by averaging method ⋮ Maximum number of limit cycles for generalized Liénard polynomial differential systems ⋮ ON THE NUMBER OF LIMIT CYCLES FOR A GENERALIZATION OF LIÉNARD POLYNOMIAL DIFFERENTIAL SYSTEMS ⋮ Limit Cycles for a Class of Polynomial Differential Systems Via Averaging Theory

Cites Work

• Unnamed Item
• Classical Liénard equations of degree \(n\geqslant 6\) can have \([\frac{n-1}{2}+2\) limit cycles]
• Limit cycles in generalized Liénard systems
• Quadratic Liénard equations with quadratic damping
• Averaging methods for finding periodic orbits via Brouwer degree.
• Mathematical problems for the next century
• Symmetry in planar dynamical systems
• Generalized quadratic Liénard equations
• Generalized cubic Liénard equations
• Limit cycles of generalized Liénard equations
• Cubic Lienard equations with linear damping
• The number of small-amplitude limit cycles of Liénard equations
• More limit cycles than expected in Liénard equations
• Limit cycles of the generalized polynomial Liénard differential equations
• Small-amplitude limit cycles of certain Liénard systems
• On the uniqueness of limit cycles surrounding one or more singularities for Liénard equations
• Small-amplitude limit cycle bifurcations for Liénard systems with quadratic or cubic damping or restoring forces
• Centennial History of Hilbert's 16th Problem
• HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS
• LIMIT CYCLES IN HIGHLY NON-LINEAR DIFFERENTIAL EQUATIONS

This page was built for publication: ON THE MAXIMUM NUMBER OF LIMIT CYCLES OF A CLASS OF GENERALIZED LIÉNARD DIFFERENTIAL SYSTEMS