Abstract
In this paper we classify the centers localized at the origin of coordinates, the cyclicity of their Hopf bifurcation and their isochronicity for the polynomial differential systems in ℝ of degree d that in complex notation z = x + iy can be written as where j is either 0 or 1, d is an arbitrary odd positive integer greater than or equal to five, λ ε ℝ, and A,B,C,D ε ℂ. Note that if d = 5 we obtain special families of quintic polynomial differential systems. © 2009 Birkhäuser Verlag Basel/Switzerland.
| Original language | English |
|---|---|
| Pages (from-to) | 657-679 |
| Journal | Nonlinear Differential Equations and Applications |
| Volume | 16 |
| DOIs | |
| Publication status | Published - 1 Oct 2009 |
Keywords
- Center
- Cyclicity
- Isochronous center
- Polynomial vector fields
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Llibre, J., & Valls, C. (2009). Classification of the centers, of their cyclicity and isochronicity for two classes of generalized quintic polynomial differential systems. Nonlinear Differential Equations and Applications, 16, 657-679. https://doi.org/10.1007/s00030-009-0029-6