On the number of limit cycles of the Lienard equation

Abstract

In this paper, we study a Lienard system of the form dot{x}=y-F(x), dot{y}=-x, where F(x) is an odd polynomial. We introduce a method that gives a sequence of algebraic approximations to the equation of each limit cycle of the system. This sequence seems to converge to the exact equation of each limit cycle. We obtain also a sequence of polynomials R_n(x) whose roots of odd multiplicity are related to the number and location of the limit cycles of the system.

10 pages, 5 figures. Submitted to Physical Review E

References in corpus (2)

• Oscillatory Behavior of the Rate of Escape through an Unstable Limit Cycle
• Instabilities, Point Attractors and Limit Cycles in a Inflationary Universe

Cited by in corpus (13)

• Systematic designing of bi-rhythmic and tri-rhythmic models in families of Van der Pol and Rayleigh oscillators
• Improving a method for the study of limit cycles of the Lienard equation
• Algebraic approximations to bifurcation curves of limit cycles for the Lienard equation
• Variational approach to a class of nonlinear oscillators with several limit cycles
• PI-controlled bioreactor as a generalized Lienard system
• Reduction of Kinetic Equations to Liénard-Levinson-Smith Form: Counting Limit Cycles
• Approximating the Amplitude and Form of Limit Cycles in the Weakly Nonlinear Regime of Lienard Systems
• Number and Amplitude of Limit Cycles emerging from {\it Topologically Equivalent} Perturbed Centers
• Mathematical Models of Bipolar Disorder
• Microscopic quantum generalization of classical Liénard oscillators
• On the determination of exact number of limit cycles in Lienard Systems
• Proving the existence of numerically detected planar limit cycles
• First Integrals vs Limit Cycles