Effects of long-range links on metastable states in a dynamic interaction network.
We introduce a model for random-walking agents on a two-dimensional periodic lattice, where the dynamic interaction network is defined using local short-range interactions and E randomly added long-range interactions. With periodic states for agents 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 results then imply that, while diversities decrease and eventually disappear with more long-range interactions, other types of diverse states can appear under this rule when networks are almost fully connected.
Center for Complex Quantum Systems and Department of Physics, University of Texas at Austin, Austin, Texas 78712, USA. suhan@physics.utexas.edu
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