Nonlinear Dynamics

, Volume 78, Issue 4, pp 2319–2329 | Cite as

Weak centers and local critical periods for a \(Z_{2}\)-equivariant cubic system

  • Ting Chen
  • Wentao Huang
  • Dacheng Ren
Original Paper


In this paper, we consider the weak center conditions and local critical periods for a \(Z_{2}\)-equivariant cubic system with eleven center conditions at the bi-center. Using the computer algebra system Mathematica, we compute the period constants and obtain the order of the weak center for every center condition separately. Finally, the number of local critical periods bifurcating from the bi-center is given by symbolic computation and numerical computation.


\(Z_{2}\)-equivariant system Period constant Weak center Critical period 

Mathematics Subject Classification

34C07 34C15 



The first author was supported by the Innovation Project of GUET Graduate Education of Guangxi(XJYC2012022). The second author was supported by the National Natural Science Foundation of China (11261013,11361017), Natural Science Foundation of Guangxi(2012GXNSFAA053003) and Guangxi Education Department Key Laboratory of Symbolic Computation and Engineering Data Processing.


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.School of Mathematics and Computing ScienceGuilin University of Electronic TechnologyGuilin China
  2. 2.Department of MathematicsHezhou UniversityHezhou China

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