Estimating the number of limit cycles for one step perturbed homogeneous degenerate centers

Authors

  • M. MolaeiDerakhtenjani Department of Applied Mathematics, University of Birjand, Birjand, Iran
  • O. RabieiMotlagh Department of Applied Mathematics, University of Birjand, Birjand, Iran
  • H.M. MohammadiNejad Department of Applied Mathematics, University of Birjand, Birjand, Iran

DOI:

https://doi.org/10.17398/2605-5686.38.1.85

Keywords:

Degenerate Center, Limit cycle, Lyapunov constant

Abstract

We consider a homogeneous degenerate center of order 2m + 1 and perturb it by a homogeneous polynomial of order 2m. We study the Lyapunov constants around the origin to estimate the number of limit cycles. To do it, we classify the parameters and study their effect on the number of limit cycles. Finally, we find that the perturbed degenerate center without any condition has at least two limit cycles, and the number of the bifurcated limit cycles could reach 2m + 3.

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References

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Published

2023-06-01

Issue

Section

Limit Circles

How to Cite

Estimating the number of limit cycles for one step perturbed homogeneous degenerate centers. (2023). Extracta Mathematicae, 38(1), 85-104. https://doi.org/10.17398/2605-5686.38.1.85