ID 110699
Author
Tsueike, Masafumi Faculty of Engineering, Tokushima University
Katsuta, Yuuji Department of Intelligent system Engineering, Ube National College of Technology
Keywords
limit cycle
bifurcation
characteristic equation
Newton's method
Content Type
Journal Article
Description
This letter describes a new computational method to obtain the bifurcation parameter value of a limit cycle in nonlinear autonomous systems. The method can calculate a parameter value at which local bifurcations; tangent, period-doubling and Neimark-Sacker bifurcations are occurred by using properties of the characteristic equation for a fixed point of the Poincaré mapping. Conventionally a period of the limit cycle is not used explicitly since the Poincaré mapping needs only whether the orbit reaches a cross-section or not. In our method, the period is treated as an independent variable for Newton's method, so an accurate location of the fixed point, its period and the bifurcation parameter value can be calculated simultaneously. Although the number of variables increases, the Jacobian matrix becomes simple and the recurrence procedure converges rapidly compared with conventional methods.
Journal Title
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
ISSN
09168508
NCID
AA10826239
Publisher
The Institute of Electronics, Information and Communication Engineers
Volume
E80-A
Issue
9
Start Page
1725
End Page
1728
Sort Key
1725
Published Date
1997-09-25
Remark
(c)1997 The Institute of Electronics, Information and Communication Engineers
IEICE Transactions Online TOP:http://search.ieice.org/
EDB ID
URL ( Publisher's Version )
FullText File
language
eng
TextVersion
Publisher
departments
Center for Administration of Information Technology
Medical Sciences
Science and Technology