  A relationship between Puiseux series satisfying an ordinary differential
equation corresponding to a polynomial dynamical system and degrees of
irreducible invariant algebraic curves is studied. A bound on the degrees of
irreducible invariant algebraic curves for a wide class of polynomial dynamical
systems is obtained. It is demonstrated that the Puiseux series near infinity
can be used to find irreducible algebraic curves explicitly. As an example, all
irreducible invariant algebraic curves for the famous FitzHugh-Nagumo system
are obtained.
