Deformed Oscillators with Two Double (Pairwise) Degeneracies of Energy Levels

A scheme is proposed which allows to obtain special $q$-oscillator models whose characteristic feature consists in possessing two differing pairs of degenerate energy levels. The method uses the model of two-parameter deformed $q,\!p$-oscillators and proceeds via appropriately chosen particular relation between $p$ and $q$. Different versions of quadratic relations $p=f(q)$ are utilized for the case which implies two degenerate pairs $E_1=E_2$ and $E_3=E_4$. On the other hand, using one fixed quadratic relation, we obtain $p$-oscillators with other cases of two pairs of (pairwise) degenerate energy levels.