  Using the evolution history of the universe, one can make constraint on the
parameter space of dynamic dark energy models. We discuss two different
parameterized dark energy models. Our results further restrict the combined
constraints obtained from supernova and WMAP observations. From the allowed
parameter space, it is found that our universe will experience an eternal
acceleration. We also estimate the bound on the physically relevant regions
both in the re-inflationary and inflationary phases.
