Similar size of slums caused by a Turing instability of migration behavior

Pelz, Peter F.; Friesen, John W.; Hartig, Jakob

doi:10.1103/physreve.99.022302

Cited by 14 publications

(28 citation statements)

References 15 publications

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“…Turing patterns are caused by instabilities in systems with reaction and diffusion and also show a characteristic size which is not imposed on the system from the outside, but is created in the system by interaction of two components. For these reasons Pelz et al [11] stated the hypothesis that slums as anthropogenic patterns can also be mapped by Turing patterns. This model would have the advantage of a small number of parameters and sizes compared to common slum models (see [25]).…”

Section: Resultsmentioning

confidence: 99%

“…In their work, Pelz et al [11] describe the formation of slums as an interaction of two social groups by two coupled differential equations. The equations in differential form are as follows:…”

Section: Model By Pelz Et Almentioning

confidence: 99%

“…This studies on the similar size of slums were recently taken up by Pelz et al [11] who put forward the hypothesis that the development of slums could be described by a Turing model. This is due to the fact, that a characteristic quantity can be observed in both Turing patterns and slums.…”

Section: Introductionmentioning

confidence: 96%

“…Pelz et al [11] propose the thesis that the formation of slums results from the interaction of two social groups with different characteristics. The interaction of both groups is described by two coupled reaction diffusion (RD) differential equations, each of which represents a social group.…”

Section: Introductionmentioning

confidence: 99%

“…To analyse these topics, the paper is structured in the following way: First, we shortly present the model of Pelz et al [11] (sec. 2.1).…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Investigation of Clustering in Turing Patterns to Describe the Spatial Relations of Slums

Hartig¹,

Friesen²,

Pelz³

2020

Preprint

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Worldwide, about one in eight people live in a slum. Empirical studies based on satellite data have identified that the size distributions of this type of settlement are similar in different cities of the Global South. Based on this result, a model was developed that describes the formation of slums with a Turing mechanism, in which patterns are created by diffusion-driven instability and the inherent characteristic length of the system is independent of boundary conditions. It has not yet been taken into account that Turing patterns usually arrange themselves regularly, while slums are often found in clusters. Therefore, this study investigates to what extent a common reaction kinetics for Turing models can be adapted to represent a locally concentrated arrangement of objects and to adapt the size distribution of the objects to the empirical results. Based on a summary of the literature and two numerical studies, it can be shown that although it is possible to adapt the model to the empirical data, this also increases the complexity of the model.

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Section: Resultsmentioning

confidence: 99%

Section: Model By Pelz Et Almentioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

“…To analyse these topics, the paper is structured in the following way: First, we shortly present the model of Pelz et al [11] (sec. 2.1).…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Investigation of Clustering in Turing Patterns to Describe the Spatial Relations of Slums

Hartig¹,

Friesen²,

Pelz³

2020

Preprint

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A possible method of selecting spatial epidemic models based on Turing’s diffusive threshold

Li,

Zhang

et al. 2023

Physica A: Statistical Mechanics and its Applications

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Widening the criteria for emergence of Turing patterns

Kuznetsov

Полежаев

2020

Chaos: An Interdisciplinary Journal of Nonlinear Science

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The classical concept for emergence of Turing patterns in reaction–diffusion systems requires that a system should be composed of complementary subsystems, one of which is unstable and diffuses sufficiently slowly while the other one is stable and diffuses sufficiently rapidly. In this work, the phenomena of emergence of Turing patterns are studied and do not fit into this concept, yielding the following results. (1) The criteria are derived, under which a reaction–diffusion system with immobile species should spontaneously produce Turing patterns under any diffusion coefficients of its mobile species. It is shown for such systems that under certain sets of types of interactions between their species, Turing patterns should be produced under any parameter values, at least provided that the corresponding spatially non-distributed system is stable. (2) It is demonstrated that in a reaction–diffusion system, which contains more than two species and is stable in absence of diffusion, the presence of a sufficiently slowly diffusing unstable subsystem is already sufficient for diffusion instability (i.e., Turing or wave instability), while its complementary subsystem can also be unstable. (3) It is shown that the presence of an immobile unstable subsystem, which leads to destabilization of waves within an infinite range of wavenumbers, in a spatially discrete case can result in the generation of large-scale stationary or oscillatory patterns. (4) It is demonstrated that under the presence of subcritical Turing and supercritical wave bifurcations, the interaction of two diffusion instabilities can result in the spontaneous formation of Turing structures outside the region of Turing instability.

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Similar size of slums caused by a Turing instability of migration behavior

Cited by 14 publications

References 15 publications

Investigation of Clustering in Turing Patterns to Describe the Spatial Relations of Slums

Investigation of Clustering in Turing Patterns to Describe the Spatial Relations of Slums

A possible method of selecting spatial epidemic models based on Turing’s diffusive threshold

Widening the criteria for emergence of Turing patterns

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