The phrase 'has gradually developed' is correct and usable in written English.
You would use it to describe how something has changed over a period of time. For example, "The technology industry has gradually developed over the last decade."
This development of the frontal lobes has gradually developed the representational space of the self in time and space.
The divergence from the ballet-master model has meant that, since de Valois, a split has gradually developed between the Royal Ballet and its school.
Mr. Peña described the film, a 1999 drama about the American Civil War, as "a great one" that has been "a little bit neglected or overlooked" but that has gradually developed a cult following.
Mr. Lower uses traditional methods for hand-pollinating, pruning and ripening, and has gradually developed an ecosystem on his ranch that's almost identical to that of the desert oases of the ancient Middle East.
The result of these and other projects is a city that has gradually developed a regional brand as a livelier place to live and do business, in a state that is doing better economically than most.
But the prospect of moving the French Open to the suburbs has gradually developed into a legitimate option or, if you are Mayor Bertrand Delanoë of Paris, a legitimate threat.
The black rats that carry plague in the highlands have gradually developed resistance to it.
But we always cook something, and my two eldest children have gradually developed their specialties.
Teams in Sweden and in Europe have gradually developed a culture, style and system of play.
With songs by Mr. Frisell, who exudes a countryish warmth, and by Mr. Carter, who manages an easy fastidiousness, the musicians have gradually developed a group dialect.
As far-flung societies have drawn closer together, they have gradually developed international standards of human rights and a patchwork legal system to judge crimes against them.
