Journal directory listing - Volume 46 Number 2 (2001/October) - Mathematics, Science & Technology【46(1&2)】
Directory
The Critical Phase Curve of Van Der Pol Equation
Author: Je-Chiang Tsai & Tai-Yih Tso(Department of Mathmatics, National Taiwan Normal University)
Vol.&No.：Vol. 46, No. 1
Date：October 2001
Pages：1-12
DOI：10.6301/JNTNU.2001.46.01
Abstract：
This article is concerned with the special trajectory
which is the leading term of the asymptotic solution of Van der Pol equation
in the phase plane for some region. We show that in the phase plane, the difference of this asymptotic solution and the limit cycle of Van der Pol equation is not greater than
as
for all
. Using this result, we can show that every trajectory of Van der Pol equation starting from y-axis with initial value bigger than that of the limit cycle gets close to the limit cycle byfrom its first time on intersecting x=1 in the four quadrant as.
Keywords：Van der Pol equation, limit cycle
《Full Text》