I don't know if there are any good materials to read up on this, I honestly don't even know where to look. I'd just like to learn about what changed policy-wise, culture-wise, economically, etc.
Initially, everybody lives in the centre, then the gentry move outwards while the poor people stay in the centres. That 'gentrified' area gradually shifts outwards and the 'doughnut' expands as the older, inner less-desirable areas get taken up by the poor (and young couples with no money) while the richer 'gentry' move further out. As those younger families get richer and larger and more gentrified they move out to the 'currently-nicer' areas.
However, eventually, the gentry find that urban renewal means that the city centres become more desirable and gentrified and they move back to the city centre while forcing the poorer outwards again. And the 'doughnut' starts expanding outwards again.
If you want to see where edge of the 'doughnut' happens to be in your city, look for the areas where the older inhabitants, the 'little old ladies', are dying off and the houses are being bought up by young couples with prams. That'll also be the area where house-prices are suddenly rising.