Abstract
We study the limit cycles of a class of cubic polynomialdifferential systems in the plane and their global shape using the averaging theory. More specifically, we analyze the global shape of the limit cycles which bifurcate: first, from a Hopf bifurcation; second, from periodic orbits of the linear center ẋ = -y, ẏ = x; and finally from periodic orbits of the cubic centers ẋ = -yh(x, y), ẏ = xh(x, y) where h(x, y) = 0 is a conic. The perturbation of these systems is made inside the class of cubic polynomial differential systems havingnon quadratic terms. © Watnam Press.
Original language | English |
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Pages (from-to) | 453-473 |
Journal | Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis |
Volume | 17 |
Issue number | 4 |
Publication status | Published - 13 Sep 2010 |
Keywords
- Averaging theory
- Cubic polynomial differential systems
- Cubic vector fields
- Limit cycles