  Many online collaboration networks struggle to gain user activity and become
self-sustaining due to the ramp-up problem or dwindling activity within the
system. Prominent examples include online encyclopedias such as (Semantic)
MediaWikis, Question and Answering portals such as StackOverflow, and many
others. Only a small fraction of these systems manage to reach self-sustaining
activity, a level of activity that prevents the system from reverting to a
non-active state. In this paper, we model and analyze activity dynamics in
synthetic and empirical collaboration networks. Our approach is based on two
opposing and well-studied principles: (i) without incentives, users tend to
lose interest to contribute and thus, systems become inactive, and (ii) people
are susceptible to actions taken by their peers (social or peer influence).
With the activity dynamics model that we introduce in this paper we can
represent typical situations of such collaboration networks. For example,
activity in a collaborative network, without external impulses or investments,
will vanish over time, eventually rendering the system inactive. However, by
appropriately manipulating the activity dynamics and/or the underlying
collaboration networks, we can jump-start a previously inactive system and
advance it towards an active state. To be able to do so, we first describe our
model and its underlying mechanisms. We then provide illustrative examples of
empirical datasets and characterize the barrier that has to be breached by a
system before it can become self-sustaining in terms of critical mass and
activity dynamics. Additionally, we expand on this empirical illustration and
introduce a new metric p---the Activity Momentum---to assess the activity
robustness of collaboration networks.
