ANALYSIS OF THE LIMIT CYCLE OF A GENERALISED VAN DER POL EQUATION BY A TIME TRANSFORMATION METHOD
作者:
G.M. Moremedi,
D.P. Mason,
期刊:
Quaestiones Mathematicae
(Taylor Available online 1994)
卷期:
Volume 17,
issue 3
页码: 349-379
ISSN:1607-3606
年代: 1994
DOI:10.1080/16073606.1994.9631770
出版商: Taylor & Francis Group
关键词: 34C05;34E15
数据来源: Taylor
摘要:
The properties of the limit cycle of a generalised van der Pol equation of the form ü + u = ε (1—u2n)u, where ε is small and n is any positive integer, are investigated by applying a time transformation perturbation method due to Burton. It is found that asnincreases the amplitude of the limit cycle oscillation decreases and its period increases. The time transformation solution is compared with the solution derived using the method of multiple scales and with a numerical solution. It is found that, to first order in ε, the time transformation solution for the limit cycle agrees better with the numerical solution than the multiple scales solution. Both perturbation solutions give the same result for the period of the limit cycle to second order in ε. The accuracy of the time transformation solution decreases as n increases.
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