Bo Sang, Qin-Long Wang, Wen-Tao Huang
Abstract:
This article presents a recursive formula for computing the n-th
singular point values of a class of 4-dimensional autonomous systems,
and establishes the algebraic equivalence between focal values and singular
point values. The formula is linear and then avoids complicated integrating
operations, therefore the calculation can be carried out by computer algebra
system such as Maple. As an application of the formula, bifurcation analysis
is made for a quadratic system with a Hopf equilibrium, which can have three
small limit cycles around an equilibrium point. The theory and methodology
developed in this paper can be used for higher-dimensional systems.
Submitted July 1, 2015. Published August 10, 2015.
Math Subject Classifications: 34C05, 34C07.
Key Words: Focal value; limit cycle; Hopf bifurcation.
Show me the PDF file (215 KB), TEX file, and other files for this article.
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Bo Sang School of Mathematical Sciences Liaocheng University Liaocheng 252059, China email: sangbo_76@163.com |
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Qing-Long Wang School of Science, Hezhou University Hezhou 542800, China email: wqinlong@163.com |
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Wen-Tao Huang School of Science, Hezhou University Hezhou 542800, China email: huangwentao@163.com |
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