  The generation of coherent superposition of distinct physical systems and the
construction of robust entangled states under decoherence are the most
experimental challenges of quantum technologies. In this work, we investigate
the behaviors of catlike states of a deformed harmonic oscillator under
dissipative decoherence. Varying the deformation parameters, we obtain catlike
states having more resistance against decoherence than catlike states of the
ordinary harmonic oscillator. Furthermore, we study nonclassical properties and
entanglement of different catlike states subjects to decoherence caused by a
dissipative interaction with a large environment. Depending on different
deformation parameters, we reveal that the nonclassical properties of catlike
states under dissipative interaction can be more retarded and preserved in the
time.
