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ASME Press Select Proceedings
International Conference on Information Technology and Computer Science, 3rd (ITCS 2011)
Editor
V. E. Muhin,
V. E. Muhin
National Technical University of Ukraine
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ISBN:
9780791859742
No. of Pages:
656
Publisher:
ASME Press
Publication date:
2011
eBook Chapter
95 Numerical Study of Limit Cycles for Three Planar Polynomial Systems
By
Xiao-Chun Hong
,
Xiao-Chun Hong
School of Mathematics and Information Science,
Qujing Normal University
, Qujing Yunnan 655011
, P. R. China
; xchhong@sina.com.cn
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Bo Wu
Bo Wu
Department of Mathematics,
Simao Teacher's College
, Puer Yunnan 665000
, P. R. China
; ynsmwb@sina.com.cn
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Page Count:
4
-
Published:2011
Citation
Hong, X, & Wu, B. "Numerical Study of Limit Cycles for Three Planar Polynomial Systems." International Conference on Information Technology and Computer Science, 3rd (ITCS 2011). Ed. Muhin, VE, & Hu, WB. ASME Press, 2011.
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Bifurcation of limit cycles for three planar polynomial systems is investigated by using both qualitative analysis and numerical exploration. The investigation is based on detection functions which are particularly effective for the planar polynomial systems. The study reveals that the perturbed Hamiltonian system (5) has only 3 limit cycles, whereas each of the two perturbed integrable non-Hamiltonian systems (6)–(7) has 4 limit cycles. By using method of numerical simulation, the distributed orderliness of these limit cycles is observed, and their nicety places are determined. The study also indicates that each of these limit cycles passes the corresponding nicety point.
Abstract
Keywords
Introduction
Detection Functions and Detection Curves
Analysis of the Unperturbed Systems
Detection Functions and Distribution of Limit Cycles of the Perturbed Systems
Conclusion
Acknowledgment
References
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