In a Hierarchical Evolutive System, a complex object emerging as the colimit of a pattern may later on take its own identity, independent from the initial pattern, as long as the change of its internal organization is progressive enough for the unity of the component to be temporally recognized on this organization. For instance, the components of a cell change in time though the cell remains 'the same'. The stability span measures the rate of change.

Let N be a component** **of level *n*+1 in a Hierarchical System. At time *t*, its state N* _{t}* is the colimit of at least one pattern P of linked objects of level

* *The *stability span* of N at *t* is the largest real *dt* such that there exists a decomposition Q* _{t}* of level

If the stability span is long enough, the change of N is gradual and ensures a temporal continuity of its internal organization allowing to recognize that the object is the same. To measure the change in a decomposition P** **of** **N from *t *to a much later time *s*, we have to compare the new state P* _{s}* of P to a decomposition R of N

In particular, let us suppose that N has emerged at *t *as the colimit of P (say, in a complexification process). Up to *t+dt*, the evolutions of N and of P are well correlated, but later on they may totally differ (e.g., P can be entirely suppressed). We say that N has taken its own *n-complex* *identity,* independent from P; its successive states have gradually changing decompositions of level *n* which are only preserved during a stability span.

The variation of the stability span of a component gives information on its rate of change. The spans are long if the system remains stable, while they shorten during development or recession phases. For instance, the decrease of the stability spans is one of the important signs in the theory of aging of an organism by a 'cascade of de-resynchronizations' proposed in (Ehresmann & Vanbremeersch 1993).