Bifurcation analysis on a class of three-dimensional quadratic systems with twelve limit cycles

Laigang Guo, Pei Yu and Yufu Chen

Applied Mathematics and Computation, 2019, vol. 363, issue C, -

Abstract: This paper concerns bifurcation of limit cycles in a class of 3-dimensional quadratic systems with a special type of symmetry. Normal form theory is applied to prove that at least 12 limit cycles exist with 6–6 distribution in the vicinity of two singular points, yielding a new lower bound on the number of limit cycles in 3-dimensional quadratic systems. A set of center conditions and isochronous center conditions are obtained for such systems. Moreover, some simulations are performed to support the theoretical results.

Keywords: 3-dimensional quadratic system; Symmetrical vector field; Normal form; Limit cycle; Isochronous center (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:363:y:2019:i:c:39

DOI: 10.1016/j.amc.2019.124577

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