  Many problems can be solved by iteration by multiple participants
(processors, servers, routers etc.). Previous mathematical models for such
asynchronous iterations assume a single function being iterated by a fixed set
of participants. We will call such iterations static since the system's
configuration does not change. However in several real-world examples, such as
inter-domain routing, both the function being iterated and the set of
participants change frequently while the system continues to function. In this
paper we extend Uresin & Dubois's work on static iterations to develop a model
for this class of "dynamic" or "always on" asynchronous iterations. We explore
what it means for such an iteration to be implemented correctly, and then prove
two different conditions on the set of iterated functions that guarantee the
full asynchronous iteration satisfies this new definition of correctness. These
results have been formalised in Agda and the resulting library is publicly
available.
