  We study a certain type of wild harmonic bundles in relation with a Toda
equation. We explain how to obtain a classification of the real valued
solutions of the Toda equation in terms of their parabolic weights, from the
viewpoint of the Kobayashi-Hitchin correspondence. Then, we study the
associated integrable variation of twistor structure. In particular, we give a
criterion for the existence of an integral structure. It follows from two
results. One is the explicit computation of the Stokes factors of a certain
meromorphic flat bundle. The other is an explicit description of the associated
meromorphic flat bundle. We use the opposite filtration of the limit mixed
twistor structure with an induced torus action.
