  We study the dynamical properties of a finite dynamical network composed of
two interacting populations, namely; extrovert ($a$) and introvert ($b$). In
our model, each group is characterized by its size ($N_a$ and $N_b$) and
preferred degree ($\kappa_a$ and $\kappa_b\ll\kappa_a$). The network dynamics
is governed by the competing microscopic rules of each population that consist
of the creation and destruction of links. Starting from an unconnected network,
we give a detailed analysis of the mean field approach which is compared to
Monte Carlo simulation data. The time evolution of the restricted degrees
$\moyenne{k_{bb}}$ and $\moyenne{k_{ab}}$ presents three time regimes and a non
monotonic behavior well captured by our theory. Surprisingly, when the
population size are equal $N_a=N_b$, the ratio of the restricted degree
$\theta_0=\moyenne{k_{ab}}/\moyenne{k_{bb}}$ appears to be an integer in the
asymptotic limits of the three time regimes. For early times (defined by
$t<t_1=\kappa_b$) the total number of links presents a linear evolution, where
the two populations are indistinguishable and where $\theta_0=1$.
Interestingly, in the intermediate time regime (defined for
$t_1<t<t_2\propto\kappa_a$ and for which $\theta_0=5$), the system reaches a
transient stationary state, where the number of contacts among introverts
remains constant while the number of connections is increasing linearly in the
extrovert population. Finally, due to the competing dynamics, the network
presents a frustrated stationary state characterized by a ratio $\theta_0=3$.
