### 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 language | English |
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Pages (from-to) | 139-145 |

Number of pages | 7 |

Journal | Transactions of the Institute of Electronics and Communication Engineers of Japan. Section E |

Volume | E66 |

Issue number | 2 |

Publication status | Published - Jan 1 1983 |

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### All Science Journal Classification (ASJC) codes

- Engineering(all)

### Cite this

*Transactions of the Institute of Electronics and Communication Engineers of Japan. Section E*,

*E66*(2), 139-145.

**ANALYTICAL DISCUSSION ON THE SELF-OSCILLATIONS IN THE VAN DER POL EQUATION FAR FROM A HARD MODE INSTABILITY POINT.** / Ezaki, Shu; Yamafuji, Kaoru; Toko, Kiyoshi; Ryu, Kouichi.

Research output: Contribution to journal › Article

*Transactions of the Institute of Electronics and Communication Engineers of Japan. Section E*, vol. E66, no. 2, pp. 139-145.

}

TY - JOUR

T1 - ANALYTICAL DISCUSSION ON THE SELF-OSCILLATIONS IN THE VAN DER POL EQUATION FAR FROM A HARD MODE INSTABILITY POINT.

AU - Ezaki, Shu

AU - Yamafuji, Kaoru

AU - Toko, Kiyoshi

AU - Ryu, Kouichi

PY - 1983/1/1

Y1 - 1983/1/1

N2 - 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.

AB - 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.

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UR - http://www.scopus.com/inward/citedby.url?scp=0020703778&partnerID=8YFLogxK

M3 - Article

VL - E66

SP - 139

EP - 145

JO - Transactions of the Institute of Electronics and Communication Engineers of Japan. Section E

JF - Transactions of the Institute of Electronics and Communication Engineers of Japan. Section E

SN - 0387-236X

IS - 2

ER -