In random network coding, the rank of a node is a random process that is
affected by a number of factors including the random coding operation, the
channel and the randomness built in the MAC and PHY. Previous approaches to
random network coding chose to only focus on the asymptotic behavior of the rank
process. For the first time, we develop a dynamical system framework for
analyzing RNC in a wireless network based on differential equations (DE). Under
the fluid approximation, ranks of different nodes are intertwined in the form of
a system of DEs that allow the study of its transient behavior. The dynamical
system framework proves to be powerful in modeling RNC with fine details present
in the channel, in the MAC/PHY or in the topology.