  In this article, we study algorithms for dynamic networks with asynchronous
start, i.e., each node may start running the algorithm in a different round.
Inactive nodes transmit only heartbeats, which contain no information but can
be detected by active nodes. We make no assumption on the way the nodes are
awakened, except that for each node u there is a time $s_u$ in which it is
awakened and starts to run the algorithm. The identities of the nodes are not
mutually known, and the network size is unknown as well.
  We present synchronization algorithms, which guarantee that after a finite
number of rounds, all nodes hold the same round number, which is incremented by
one each round thereafter. We study the time complexity and message size
required for synchronization, and specifically for simultaneous
synchronization, in which all nodes synchronize their round numbers at exactly
the same round.
  We show that there is a strong relation between the complexity of
simultaneous synchronization and the connectivity of the dynamic graphs: With
high connectivity which guarantees that messages can be broadcasted in a
constant number of rounds, simultaneous synchronization by all nodes can be
obtained by a deterministic algorithm within a constant number of rounds, and
with messages of constant size. With a weaker connectivity, which only
guarantees that the broadcast time is proportional to the network size, our
algorithms still achieve simultaneous synchronization, but within linear time
and long messages.
  We also discuss how information on the network size and randomization may
improve synchronization algorithms, and show related impossibility results.
