  A remarkable phenomenon in the time evolution of many networks such as
cultural, political, national and economic systems, is the recurrent transition
between the states of union and division of nodes. In this work, we propose a
phenomenological modeling, inspired by the maxim "long union divides and long
division unites", in order to investigate the evolutionary characters of these
networks composed of the entities whose behaviors are dominated by these two
events. The nodes are endowed with quantities such as identity, ingredient,
richness (power), openness (connections), age, distance, interaction etc. which
determine collectively the evolution in a probabilistic way. Depending on a
tunable parameter, the time evolution of this model is mainly an alternative
domination of union or division state, with a possible state of final union
dominated by one single node.
