Abstract
We consider centralized networks composed of multiple satellites arranged around a few dominating super-egoistic centers. These so-called empires are organized using a divide and rule framework enforcing strong center–satellite interactions while keeping the pairwise interactions between the satellites sufficiently weak. We present a stochastic stability analysis, in which we consider these dynamical systems as stable if the centers have sufficient resources while the satellites have no value. Our model is based on a Hopfield type network that proved its significance in the field of artificial intelligence. Using this model, it is shown that the divide and rule framework provides important advantages: it allows for completely controlling the dynamics in a straight-forward way by adjusting center–satellite interactions. Moreover, it is shown that such empires should only have a single ruling center to provide sufficient stability. To survive, empires should have switching mechanisms implementing adequate behavior models by choosing appropriate local attractors in order to correctly respond to internal and external challenges. By an analogy with Bose–Einstein condensation, we show that if the noise correlations are negative for each pair of nodes, then the most stable structure with respect to noise is a globally connected network. For social systems, we show that controllability by their centers is only possible if the centers evolve slowly. Except for short periods when the state approaches a certain stable state, the development of such structures is very slow and negatively correlated with the size of the system’s structure. Hence, increasing size eventually ends up in the “control trap.”
Highlights
The introduction of the divide and rule concept is partly attributed to the Florentine diplomat and political theorist Niccolò Machiavelli who explained in his 16th-century political treatise The Prince (Il Principe)1,2 to Lorenzo di Piero de’ Medici, at that time the ruler of Florence, how to increase and maintain his power
We show that the divide and rule framework provides important advantages: it allows for completely controlling the dynamics in a straightforward way by adjusting center–satellite interactions
It is shown that the probability to be in this state within a time T can be estimated by an interesting relation, which admits an analogy with physics
Summary
The introduction of the divide and rule concept ( divide and conquer or divide et impera in its Latin formulation) is partly attributed to the Florentine diplomat and political theorist Niccolò Machiavelli who explained in his 16th-century political treatise The Prince (Il Principe) to Lorenzo di Piero de’ Medici, at that time the ruler of Florence, how to increase and maintain his power. The centers exercise control over the lower-level satellite components directly using a binary power hierarchy realized by the application of a strict divide and rule framework allowing for the active supervision of the lower-level components To their importance with respect to social structures, we would like to mention here that divide and rule networks are omnipresent in the natural sciences, for example, as dynamical models for gene regulation and neural networks.. To their importance with respect to social structures, we would like to mention here that divide and rule networks are omnipresent in the natural sciences, for example, as dynamical models for gene regulation and neural networks.16,17 In this context, it was shown that such networks can generate complicated (including chaotic) attractors and exhibit different non-trivial bifurcations.
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