SMALL AMPLITUDE LIMIT-CYCLES OF THE GENERALIZED MIXED RAYLEIGH-LIENARD OSCILLATOR

This paper is concerned with the generalized mixed (Rayleigh-Lienard) oscillator equations of the form x + x + b30x3 + (a1 + b21x2 + b41x4 + b03x2)x = 0. The problem is to obtain the maximum possible number of limit cycles under perturbation of the coefficients arising in these equations. An algorithm is implemented on a computer to determine a so-called focal basis. Estimates can then be obtained for the number of limit cycles which may be bifurcated in a small region of the origin. It is shown that at most three small amplitude limit cycles may be bifurcated.