About Duffing equation Is there a relation between Duffing equation and Van der Pol equation? My second question is what is the application(s) of stochastic Duffing equn. in practice ?

First part:

Both are non-linear dynamic oscillations. Van der Pol is smooth continuous but Duffing has sudden "snap-through" bi-stable behavior like the Belleville spring in the negative stiffness region. The mode of energy transfer is abrupt and chaotic at places and quite unlike smooth second order linear systems due to the cube term as for the stiffening spring. Their difference can be seen markedly in their respective phase portraits.