Geographia Polonica (1986) vol. 52

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Stability versus complexity in self-organizing spatial systems

Ryszard Domański

Geographia Polonica (1986) vol. 52, pp. 135-146

Abstract

This paper investigates the variation of stability connected with the process ofcomplication of the organization of spatial systems.

Two basic notions used in the investigation are conceived here in a differentway than in standard systems analysis, although we base ourselves on it. Hence,they require new definitions. The notions are: stability and equilibrium. Stabilityis meant as the convergence with the state of equilibrium. A system is less stableif it diverges more from the state of equilibrium. By the equilibrium of a systemwe understand mutual adjustment of its subsystems (elements, connections). Theequilibrium, as it is conceived here, cannot be defined, however, in a unique way.It can be determined only by the comparison with the assumed reference system.We assume that the system is in equilibrium if its subsystems are adjusted in the sameor higher degree than that of reference system. In spatial context, the equilibriummeans the same or lesser spatial differentiation in comparison with the referencesystem.

Defined in this way, the equilibrium can be a desired state of spatial organizationof a system, and the investigation of instability can be essential for the determinationof intervention needed to direct the system towards the state of equilibrium.

Spatial systems considered in this paper are self-organizing in the sense ofPrigogine's theory. They are open and linked with the environment, far fromuniformity, and the interactions between their elements reveal nonlinearities.

Spatial organization complicates as the system develops. This implies the changeof its stability. The investigation of stability gives insight in important propertiesof spatial systems.

Although the investigation of stability against complexity was the starting pointof this paper, its final result turned out to be more significant from other pointof view. It enabled the modification of an acknowledged theorem of regionalscience.

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Ryszard Domański, Academy of Economics Poznań, Department of Spatial and Environmental Economics al. Niepodległości 10, 60-967 Poznań, Poland