Bifurcation of limit cycles, classification of centers and isochronicity for a class of non-analytic quintic systems

被引：0
作者：
Li Feng
Qiu Jianlong
Jing Li
机构：
[1] Linyi University,
来源：
Nonlinear Dynamics | 2014年 / 76卷
关键词：
Non-analytic; Center–focus problem; Lyapunov constant; Isochronous center;
D O I：
暂无
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学科分类号：
摘要：
Inspired by Llibre and Vallls (in J. Math. Anal. Appl. 357:427–437, 2009), the conditions of center and isochronous center at the origin for a class of non-analytic quintic systems are studied in this paper. By a transformation, we first transform the systems into analytic systems, then sufficient and necessary conditions for the origin of the systems being a center are obtained. The fact that 11 limit circles could be bifurcated is proved. A complete classification of the sufficient and necessary conditions is given for the origin of the systems being an isochronous center.
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页码：183 / 197
页数：14
相关论文
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  • [1] Lamarque C.(2012)An upper bound for validity limits of asymptotic analytical approaches based on normal form theory Nonlinear Dyn. 123 77-96
  • [2] Touzé C.(2012)New limit cycles of dry friction oscillators under harmonic load Nonlinear Dyn. 126 351-368
  • [3] Thomas O.(1999)Isochronous centers of s linear center perturbed by fourth degree homogeneous polynomial Bull. Sci. Math. 38 39-53
  • [4] Pascal M.(2000)Isochronous centers of s linear center perturbed by fifth degree homogeneous polynomial Bull. Sci. Math. 211 190-212
  • [5] Chavarriga J.(1999)A class of reversible cubic systems with an isochronous center Comput. Math. Appl. 246 2192-2204
  • [6] Giné J.(1997)An explicit expression of the first Lyapunov and period constants with applications J. Math. Anal. Appl. 71 3119-3128
  • [7] Garcia I.(2009)Classification of the centers, their cyclicity and isochronicity for a class of polynomial differential systems generalizing the linear systems with cubic homogeneous nonlinearities J. Differ. Equ. 357 427-437
  • [8] Chavarriga J.(2009)Classification of the centers and isochronous centers for a class of quartic-like systems Nonlinear Anal. 16 657-679
  • [9] Giné J.(2009)Classification of the centers, their cyclicity and isochronicity for the generalized quadratic polynomial differential systems J. Math. Anal. Appl. 45 671-682
  • [10] Garcia I.(2009)Classification of the centers, of their cyclicity and isochronicity for two classes of generalized quintic polynomial differential systems Nonlinear Differ. Equ. Appl. 25 295-302
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