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- Title
Cyclicity of period annulus for a class of quadratic reversible systems with a nonrational first integral.
- Authors
Cen, Xiuli; Liu, Changjian; Sun, Yangjian; Wang, Jihua
- Abstract
In this paper, we study the quadratic perturbations of a one-parameter family of reversible quadratic systems whose first integral contains the logarithmic function. By the criterion function for determining the lowest upper bound of the number of zeros of Abelian integrals, we obtain that the cyclicity of either period annulus is two. To the best of our knowledge, this is the first result for the cyclicity of period annulus of the one-parameter family of reversible quadratic systems whose first integral contains the logarithmic function. Moreover, the simultaneous bifurcation and distribution of limit cycles from two-period annuli are considered.
- Subjects
ABELIAN functions; LOGARITHMIC functions; INTEGRALS; QUADRATIC differentials; CHEBYSHEV systems; BIFURCATION diagrams; LIMIT cycles
- Publication
Proceedings of the Royal Society of Edinburgh: Section A: Mathematics, 2023, Vol 153, Issue 5, p1706
- ISSN
0308-2105
- Publication type
Article
- DOI
10.1017/prm.2022.70