An Analytical Discussion on the Self-Oscillations in the Van der Pol Equation Far from a Hard Mode Instability Point

Shu EZAKI, Kaoru YAMAFUJI, Kiyoshi TOKO, Kouichi RYU

Summary :

A nonperturbative method is presented for describing approximately the behavior of a self-oscillation of electric voltage in the Van der Pol equation over a wide range of the value of external parameter µ. To express an appreciably distorted wave form for the steady self-oscillation at µ1, a phase F of the voltage x, defined by x2A cos F (ωt), is approximated by a combination of several straight lines as a function of ωt from 0 to 2π with several numerical coefficients determined mainly from asymptotic behaviors of x for µ1 and µ1. It is shown that the resultant expression for x can describe well the numerical result over the wide range of µ. A bursting phenomenon induced by an oscillation of µ with a long period is also discussed on the basis of the present method, and the analytical results are in good agreement with the numerical ones.

• Publication: IEICE TRANSACTIONS on transactions Vol.E66-E No.2 pp.139-145
• Publication Date: 1983/02/25
• Type of Manuscript: PAPER
• Category: General

Authors

Shu EZAKI
Kaoru YAMAFUJI
Kiyoshi TOKO
Kouichi RYU

Keyword