Limit cycles of polynomial systems with homogeneous non-linearities

doi:10.1016/0022-247X(89)90021-8

Journal of Mathematical Analysis and Applications

Volume 142, Issue 2, September 1989, Pages 573-590

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Abstract

We study the class of vector fields of the form x = P₁(x, y) + P_n(x, y), y = Q₁(x, y) + Q_n(x, y), where P_k and Q_k are real homogeneous polynomials of degree k, n ⩾ 2, and the origin is a non-degenerate critical point of index 1. For this class of vector fields we give four theorems about their limit cycles.

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^∗: The second author has been partially supported by the CAICYT under Grant 3534/83.C3.