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

Research output: Contribution to journalArticlepeer-review

Abstract

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 mu . To express an appreciably distorted wave form for the steady self-oscillation at mu greater than greater than 1, a phase F of the voltage x, defined by x equals 2 A cos F ( omega t), is approximated by a combination of several straight lines as a function of omega t from 0 to 2 pi with several numerical coefficients determined mainly from asymptotic behaviors of x for mu less than less than 1 and mu greater than greater than 1. It is shown that the resultant expression for x can describe well the numerical result over the wide range of mu . A bursting phenomenon induced by an oscillation of mu 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.

Original languageEnglish
Pages (from-to)139-145
Number of pages7
JournalTransactions of the Institute of Electronics and Communication Engineers of Japan. Section E
VolumeE66
Issue number2
Publication statusPublished - Jan 1 1983
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Engineering(all)

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