Nonsingular parametric oscillators Darboux-related to the classical   harmonic oscillator
  Interesting nonsingular parametric oscillators which are Darboux related to the classical harmonic oscillator and have periodic dissipative/gain features are identified through a modified factorization method. The same method is applied to the upside-down (hyperbolic) `oscillator' for which the obtained Darboux partners show transient underdamped features 
H.C.Rosu, O.Cornejo-Perez, P. Chen
math-ph math.MP