The concepts of Statistical Physics have been applied in several ways to the study of the economic and social problems. This has generated divers approximations and models that may be applied under different circumstances and with different objectives.
One of them is the study of the social hierarchies considered in the Bonabeau model. The emergent collective behaviour of the elements integrating the social systems has been the primordial characteristic to consider the application of the statistical physics concepts in their analysis.
The model of social hierarchies of Bonabeau is based in the creation of artificial societies that follow certain group of rules. (1) This model is able to describe the transition of societies from egaletarian to more hierarchical ones. The artificial agents that appear in the results of this approach may be substituted by animals, individuals, communities, countries, etc., depending the problem that is being analyzed.
However, despite the simplicity of the model, it has showed not be so close to reality. In order to improuve the model it has been modified, over all in the rules that follow the agents, giving approaches more realistics and with extended applicability (2).
Due to the complexity of the system, and the idea of introducing a ”lattice with dynamical distribution of attractive sites coupled with the agent distribution”(2), and in order to improuve the analysis, may be good propose the use of a dynamical network that helps to link the agents and the sites by means of dynamic links and dynamics sites, in such a form that each agent may have a memory of their movements but also a knowledge of the movements of the other agents.
(1) E. Bonabeau, G. Theraulaz, J.L. Deneubourg, Physica A 217 (1995) 1157.
(2) G.G. Naumis, M. del Castillo-Mussot, L.A. Perez, G.J.Vazquez, Physica A 369 (2006) 789-798