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.
|Journal||Nonlinear Differential Equations and Applications|
|Publication status||Published - 1 Oct 2009|
- Isochronous center
- Polynomial vector fields
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