  This paper aims to provide a systemic analysis to social opinion dynamics
subject to individual biases. As a generalization of the classical DeGroot
social interactions, defined by linearly coupled dynamics of peer opinions that
evolve over time, biases add to state-dependent edge weights and therefore lead
to highly nonlinear network dynamics. Previous studies have dealt with
convergence and stability analysis of such systems for a few specific initial
node opinions and network structures, and here we focus on how individual
biases affect social equilibria and their stabilities. First of all, we prove
that when the initial network opinions are polarized towards one side of the
state space, node biases will drive the opinion evolution to the corresponding
interval boundaries. Such polarization attraction effect continues to hold
under even directed and switching network structures. Next, for a few
fundamental network structures, some important interior network equilibria are
presented explicitly for a wide range of system parameters, which are shown to
be locally unstable in general. Particularly, the interval centroid is proven
to be unstable regardless of the bias level and the network topologies.
