Electron. J. Diff. Equ.,
Vol. 2015 (2015), No. 209, pp. 111.
Computation of focal values and stability analysis
of 4dimensional systems
Bo Sang, QinLong Wang, WenTao Huang
Abstract:
This article presents a recursive formula for computing the nth
singular point values of a class of 4dimensional 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 higherdimensional systems.
Submitted July 1, 2015. Published August 10, 2015.
Math Subject Classifications: 34C05, 34C07.
Key Words: Focal value; limit cycle; Hopf bifurcation.
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Bo Sang
School of Mathematical Sciences
Liaocheng University
Liaocheng 252059, China
email: sangbo_76@163.com


QingLong Wang
School of Science, Hezhou University
Hezhou 542800, China
email: wqinlong@163.com


WenTao Huang
School of Science, Hezhou University
Hezhou 542800, China
email: huangwentao@163.com

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