  In some social networks, the opinion forming is based on its own and
neighbors' (initial) opinions, whereas the evolution of the individual opinions
is also influenced by the individual's past opinions in the real world. Unlike
existing social network models, in this paper, a novel model of opinion
dynamics is proposed, which describes the evolution of the individuals'
opinions not only depends on its own and neighbors' current opinions, but also
depends on past opinions. Memory and memoryless communication rules are
simultaneously established for the proposed opinion dynamics model. Sufficient
and/or necessary conditions for the equal polarization, consensus and
neutralizability of the opinions are respectively presented in terms of the
network topological structure and the spectral analysis. We apply our model to
simulate Kahneman's seminal experiments on choices in risky and riskless
contexts, which fits in with the experiment results. Simulation analysis shows
that the memory capacity of the individuals is inversely proportional to the
speeds of the ultimate opinions formational.
