“…Firstly, we consider a damped periodically driven pendulum, applying our results obtained in [23]. Secondly, we study a driven pendulum with van der Pol's type damping, generalizing our previous studies [30,31]. Since we compute non-linear resonances (2) by the Krylov-Bogoliubov-Mitropolsky (KBM) method, which applies to polynomial non-linearities only, we have to expand the typical pendulum term sin(y), appearing in the function f y, dy dτ , τ; c in (1), and consider contributions from terms of the expansion sin(y) ∑ n k=1 c k y 2k+1 for growing n. In Section 3, we compute bifurcation sets D n (c) = 0, where D n is a non-linear function of parameters c and n + 1 is the number of terms in the expansion of sin(y).…”