Improving a method for the study of limit cycles of the Lienard equation

Abstract

In recent papers we have introduced a method for the study of limit cycles of the Lienard system: dot{x}=y-F(x), dot{y}=-x, where F(x) is an odd polynomial. The method gives a sequence of polynomials R_n(x), whose roots are related to the number and location of the limit cycles, and a sequence of algebraic approximations to the bifurcation set of the system. In this paper, we present a variant of the method that gives very important qualitative and quantitative improvements.

11 pages, 4 figures

References in corpus (1)

• On the number of limit cycles of the Lienard equation

Cited by in corpus (4)

• Variational approach to a class of nonlinear oscillators with several limit cycles
• PI-controlled bioreactor as a generalized Lienard system
• On the determination of exact number of limit cycles in Lienard Systems
• Extreme events in the Lienard system with asymmetric potential: An in-depth exploration