  We consider a system of two coupled oscillators one of which is driven
parametrically and investigate both classical and quantum dynamics within
Floquet description. Characteristic changes in the time evolution of the
quantum fluctuations are observed for dynamically stable and unstable regions.
Dynamical instability generated by the parametrically driven oscillator leads
to infinite temperature thermalization of the undriven oscillator which is
evident from the equi-partitioning of energy, reduced density matrix and
saturation of entanglement entropy. We also confirm that the classical Lyapunov
exponent is correctly captured from the growth rate of `unequal time
commutator' of dynamical variables which indicates thermalization stems from
the instability in quantum system.
