Abstract
We consider planar cubic systems with a unique rest point of center-focus type and constant angular velocity. For such systems we obtain an affine classification in three families, and, for two of them, their corresponding phase portraits on the Poincaré sphere. We also prove that for two of these families there is uniqueness of limit cycle. With respect the third family, we give the bifurcation diagram and phase portraits on the Poincaré sphere of a one-parameter sub-family exhibiting at least two limit cycles. © 2004 Elsevier Inc. All rights reserved.
Original language | English |
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Pages (from-to) | 391-404 |
Journal | Journal of Mathematical Analysis and Applications |
Volume | 303 |
DOIs | |
Publication status | Published - 15 Mar 2005 |
Keywords
- Bifurcation
- Center
- Cubic system
- Limit cycle