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Abstract
We introduce cluster dynamical models of conflicts in which only the largest cluster
can be involved in an action. This mimics the situations in which an attack is planned
by a central body, and the largest attack force is used. We study the model in its
annealed random graph version, on a fixed network, and on a network evolving through
the actions. The sizes of actions are distributed with a power-law tail, however,
the exponent is non-universal and depends on the frequency of actions and sparseness
of the available connections between units. Allowing the network reconstruction over
time in a self-organized manner, e.g., by adding the links based on previous liaisons
between units, we find that the power-law exponent depends on the evolution time of
the network. Its lower limit is given by the universal value 5/2, derived analytically
for the case of random fragmentation processes. In the temporal patterns behind the
size of actions we find long-range correlations in the time series of number of clusters
and non-trivial distribution of time that a unit waits between two actions. In the
case of an evolving network the distribution develops a power-law tail, indicating
that through the repeated actions, the system develops internal structure which is
not just more effective in terms of the size of events, but also has a full hierarchy
of units.