  We study the behavior of a generalized consensus dynamics on a temporal
network of interactions, the activity driven network with attractiveness. In
this temporal network model, agents are endowed with an intrinsic activity $a$,
ruling the rate at which they generate connections, and an intrinsic
attractiveness $b$, modulating the rate at which they receive connections. The
consensus dynamics considered is a mixed voter/Moran dynamics. Each agent,
either in state $0$ or $1$, modifies his/her state when connecting with a peer.
Thus, an active agent copies his/her state from the peer (with probability $p$)
or imposes his/her state to him/her (with the complementary probability $1-p$).
Applying a heterogeneous mean-field approach, we derive a differential equation
for the average density of voters with activity $a$ and attractiveness $b$ in
state $1$, that we use to evaluate the average time to reach consensus and the
exit probability, defined as the probability that a single agent with activity
$a$ and attractiveness $b$ eventually imposes his/her state to a pool of
initially unanimous population in the opposite state. We study a number of
particular cases, finding an excellent agreement with numerical simulations of
the model. Interestingly, we observe a symmetry between voter and Moran
dynamics in pure activity driven networks and their static integrated
counterparts that exemplifies the strong differences that a time-varying
network can impose on dynamical processes.
