  We introduce a model for random-walking nodes on a periodic lattice, where
the dynamic interaction network is defined from local interactions and E
randomly-added long-range links. With periodic states for nodes and an
interaction rule of repeated averaging, we numerically find two types of
metastable states at low- and high-E limits, respectively, along with consensus
states. If we apply this model to opinion dynamics, metastable states can be
interpreted as sustainable diversities in our societies, and our result then
implies that, while diversities decrease and eventually disappear with more
long-range connections, another type of states of diversities can appear when
networks are almost fully-connected.
