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Rise of nations: Why do empires expand and fall?

S Vakulenko¹, D A Lyakhov², A G Weber³

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Summary

This summary is machine-generated.

Centralized networks using a "divide and rule" strategy offer control advantages. Optimal stability in these "empires" requires a single center and slow-evolving central nodes to avoid a "control trap".

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Area of Science:

Network dynamics
Artificial intelligence
Complex systems

Background:

Centralized networks with super-egoistic centers and satellite nodes are modeled.
A divide and rule framework enforces strong center-satellite and weak satellite-satellite interactions.
The model is based on a Hopfield-type network, significant in artificial intelligence.

Purpose of the Study:

To analyze the stochastic stability of centralized networks organized in an "empire" structure.
To investigate the impact of the divide and rule framework on network control and stability.
To determine optimal configurations for network survival and responsiveness.

Main Methods:

Stochastic stability analysis of dynamical systems.
Utilizing a Hopfield-type network model.
Employing analogies with Bose-Einstein condensation for noise correlation analysis.

Main Results:

The divide and rule framework allows straightforward control by adjusting center-satellite interactions.
A single ruling center ensures maximum stability.
Negative noise correlations favor globally connected networks, analogous to Bose-Einstein condensation.
Controllability in social systems requires slow evolution of central nodes, risking a "control trap" with increasing system size.

Conclusions:

Centralized network structures can be effectively controlled using a divide and rule approach.
Optimal network design involves a single center and mechanisms for behavioral adaptation.
System size and central node dynamics critically influence long-term stability and controllability.