This post is a sketch of a model of secular stagnation; and of bubbles that burst and get replaced by different bubbles. I don't formalise the model mathematically, because I don't have a comparative (or absolute) advantage at that sort of thing. But I think it could be formalised fairly easily.
Start with a model where the equilibrium interest rate is below the growth rate of the economy. For example, an overlapping generations model, where the young produce consumption goods, and want to save for their old age, but real investment opportunities either don't exist, or else yield a very low rate of return.