Electron. J. Diff. Equ., Vol. 2016 (2016), No. 109, pp. 1-11.

Limit cycles bifurcated from a center in a three dimensional system

Bo Sang, Brigita Fercec, Qin-Long Wang

Based on the pseudo-division algorithm, we introduce a method for computing focal values of a class of 3-dimensional autonomous systems. Using the $\epsilon^1$-order focal values computation, we determine the number of limit cycles bifurcating from each component of the center variety (obtained by Mahdi et al). It is shown that at most four limit cycles can be bifurcated from the center with identical quadratic perturbations and that the bound is sharp.

Submitted September 25, 2015. Published April 26, 2016.
Math Subject Classifications: 34C05, 34C07.
Key Words: Focal value; limit cycle; Hopf bifurcation; center.

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Bo Sang
School of Mathematical Sciences
Liaocheng University
email: sangbo_76@163.com
Brigita Fercec
Faculty of Energy Technology
University of Maribor
Hocevarjev trg 1, 8270 Krsko, Slovenia
email: brigita.fercec@gmail.com
Qin-Long Wang
School of Science
Hezhou University
Hezhou 542800, China
email: wqinlong@163.com

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