Limit Cycles Analysis in a Fifth-Order Vector Field with Asymmetric Perturbation Terms
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.
KeywordsLimit cycle Five-order vector field Detection function Numerical exploration Qualitative analysis
This work was financially supported by the Natural Science Foundation of China (Grant No. 11761075).
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