Abstract:

We consider the generalized Lienard polynomial differential equation $x' = y,  y' = -g(x)-f(x)y,$  where $f$ and $g$ are polynomials of degree $m$ and $n$ respectively. We characterize all the values of $m$ and $n$ for which such differential equations have algebraic limit cycles.

This is a joint work with Jiazhong Yang and Xiang Zhang.

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