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Limit Cycles Analysis in a Fifth-Order Vector Field with Asymmetric Perturbation Terms

  • Yanjie Wang
  • Lijun Hong
  • Xiaochun HongEmail author
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1074)

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.

Keywords

Limit cycle Five-order vector field Detection function Numerical exploration Qualitative analysis 

Notes

Acknowledgment

This work was financially supported by the Natural Science Foundation of China (Grant No. 11761075).

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.School of Statistics and MathematicsYunnan University of Finance and EconomicsKunmingPeople’s Republic of China

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