  For a commutative non-autonomous dynamical system we show that topological
transitivity of the non-autonomous system induced on probability measures
(hyperspaces) is equivalent to the weak mixing of the induced systems. Several
counter examples are given for the results which are true in autonomous but
need not be true in non-autonomous systems. Wherever possible sufficient
conditions are obtained for the results to hold true. For a commutative
periodic non-autonomous system on intervals, it is proved that weakly mixing
implies Devaney chaos. Given a periodic non-autonomous system, it is shown that
sensitivity is equivalent to some stronger forms of sensitivity on a closed
unit interval.
