Comparison of the number of limit cycles of generalized Lienard systems obtained by various methods

The article presents the computation data for the maximum number of low-amplitude limit cycles for two types of generalized polynomial systems of differential equations that formally coincide in a certain set of particular cases. The first technique is based on the method of averaging and our own algorithm for calculating Lyapunov quantities computation, the second technique - on investigation of influence of small perturbations on the Hamiltonian system. Contrary to expectations, various techniques in some cases give inconsistent results.