Electron. J. Diff. Equ., Vol. 2015 (2015), No. 209, pp. 1-11.

Computation of focal values and stability analysis of 4-dimensional systems

Bo Sang, Qin-Long Wang, Wen-Tao Huang

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.

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Bo Sang
School of Mathematical Sciences
Liaocheng University
Liaocheng 252059, China
email: sangbo_76@163.com
Qing-Long Wang
School of Science, Hezhou University
Hezhou 542800, China
email: wqinlong@163.com
Wen-Tao Huang
School of Science, Hezhou University
Hezhou 542800, China
email: huangwentao@163.com

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