Generalized cubic Liénard equations Original Research Article

This article presents a new method for determining the Liapunov quantities of Liénard systems with either cubic damping or restoring terms. The first eleven quantities have been computed on a PC, whereas the algorithm used previously requires the use of high powered computers with lots of memory. The reduction part of the algorithm is simplified by expressing the Liapunov quantities in a special form. The maximum number of small-amplitude limit cycles which may be bifurcated from the origin is given for certain systems.