https://doi.org/10.1140/epjs/s11734-025-01747-0
Regular Article
In memoriam Hermann Haken: synergetics and self-organisation in complex systems
Selforganized criticality in spatial systems
Ferdinand-Steinbeis-Institute, Filderhauptstrasse 142, 70599, Stuttgart, Germany
Received:
14
April
2025
Accepted:
6
June
2025
Published online:
28
July
2025
Why are populations concentrated in settlements and cities? Why were there only a few cities worldwide with over one million inhabitants in the nineteenth century, while today there are well over three hundred? The growth of metropolitan regions is primarily due to net migration flows into cities. Population flows are based on individuals’ decisions to relocate. Individuals do not make decisions independently of one another. The dependence of migration decisions on synergistic effects leads to self-reinforcing processes that can potentially trigger shocks in urban development, phase transitions, and settlement instabilities. Based on the synergetic framework of H. Haken, it will be investigated under which conditions or system parameters the homogeneous population distribution becomes unstable, and which path the system trajectory preferentially takes when the homogeneous solution becomes unstable. Our simulations show that the assumption of a decreasing marginal spatial utility function appears most appropriate. The critical agglomeration parameter, which determines the spatial phase transition, is calculated. In the long run, the settlement system approaches a Pareto distribution if we require that the agglomeration parameter assumes its critical value. This means that the settlement system satisfies the condition of self-organized criticality (SOC). The critical agglomeration parameter of the settlement system determines the scale invariance without the need to set the control parameters to precise values. The Pareto distribution is the result of a dynamic self-organization process. Starting from a spatial instability of the homogeneous population distribution, different spatial modes compete and drive the spatial system towards its critical point as an attractor.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
