Abstract
The limit cycle bifurcation of a plane fifth-order vector field with double homoclinic polycyclic rings is studied by qualitative analysis and numerical exploration. This study is based on a detection function that is particularly effective for perturbed planar polynomial system. The research shows that a class of five-order vector field has 5 limit cycles under asymmetric disturbance. The asymmetric perturbation here has 4 arbitrary parameters. Using the numerical simulation method, the distributed orderliness of the 5 limit cycles is observed. This will help to further study Hilbert’s 16th question.
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Acknowledgment
This work was financially supported by the Natural Science Foundation of China (Grant No. 11761075).
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Wang, Y., Hong, L., Hong, X. (2020). Limit Cycles Analysis in a Fifth-Order Vector Field with Asymmetric Perturbation Terms. In: Liu, Y., Wang, L., Zhao, L., Yu, Z. (eds) Advances in Natural Computation, Fuzzy Systems and Knowledge Discovery. ICNC-FSKD 2019. Advances in Intelligent Systems and Computing, vol 1074. Springer, Cham. https://doi.org/10.1007/978-3-030-32456-8_56
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DOI: https://doi.org/10.1007/978-3-030-32456-8_56
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