Analysis of Generalized Lienard Oscillators

Exploring the behavior of generalized Lienard oscillators with dissipation

Abstract

A systematic qualitative study of generalized Lienard oscillators is performed here proposed by C. [J.Math.Phys.56,012903 (2015)] Quesne. It also explores the influence of dissipation. We show that while the first potential admits a pair of equilibrium points, one of which is usually a centre for both signs of the coupling strength λ, the other points to a centre for λ < 0 but a saddle λ > 0 by performing a local analysis of the governing potentials. A significant finding is that in the presence of a periodic force term f cos ωt.