  Time-evolution of the vibrational states of two interacting harmonic
oscillators in the local mode scheme is presented. A local-to-normal mode
transition (LNT) is identified and studied from the time dependent point of
view. The LNT is established as a polyad breaking phenomenon from the local
point of view for the stretching degrees of freedom in a triatomic molecule.
This study is carried out in the algebraic representation of bosonic operators.
The dynamics of the states are determined via the solutions of the
corresponding nonlinear Ermakov equation. Application of this formalism to
H$_2$O, CO$_2$, O$_3$ and NO$_2$ molecules in the adiabatic, sudden and linear
regime is considered.
