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

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Abstract

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.

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Acknowledgments

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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Authors and Affiliations

  1. School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin , 541004, China

    Ting Chen, Wentao Huang & Dacheng Ren

  2. Department of Mathematics, Hezhou University, Hezhou , 542800, China

    Wentao Huang

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  1. Ting Chen
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  2. Wentao Huang
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  3. Dacheng Ren
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Correspondence to Wentao Huang.

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Chen, T., Huang, W. & Ren, D. Weak centers and local critical periods for a \(Z_{2}\)-equivariant cubic system. Nonlinear Dyn 78, 2319–2329 (2014). https://doi.org/10.1007/s11071-014-1560-5

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  • DOI: https://doi.org/10.1007/s11071-014-1560-5

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