Turing instability in an economic-demographic dynamical system may lead to pattern formation on a geographical scale

Spatial distribution of the human population is distinctly heterogeneous, e.g. showing significant difference in the population density between urban and rural areas. In the historical perspective, i.e. on the timescale of centuries, the emergence of densely populated areas at their present locations is widely believed to be linked to more favourable environmental and climatic conditions. In this paper, we challenge this point of view. We first identify a few areas at different parts of the world where the environmental conditions (quantified by the temperature, precipitation and elevation) show a relatively small variation in space on the scale of thousands of kilometres. We then examine the population distribution across those areas to show that, in spite of the approximate homogeneity of the environment, it exhibits a significant variation revealing a nearly periodic spatial pattern. Based on this apparent disagreement, we hypothesize that there may exist an inherent mechanism that may lead to pattern formation even in a uniform environment. We consider a mathematical model of the coupled demographic-economic dynamics and show that its spatially uniform, locally stable steady state can give rise to a periodic spatial pattern due to the Turing instability, the spatial scale of the emerging pattern being consistent with observations. Using numerical simulations, we show that, interestingly, the emergence of the Turing patterns may eventually lead to the system collapse.

Авторы
Zincenko A.1, 2 , Petrovskii S. 1 , Volpert V. 3, 4, 5 , Banerjee M.6
Издательство
ROYAL SOC
Номер выпуска
177
Язык
Английский
Статус
Опубликовано
Номер
20210034
Том
18
Год
2021
Организации
  • 1 Univ Leicester, Sch Math & Actuarial Sci, Leicester LE1 7RH, Leics, England
  • 2 Univ Birmingham, Sch Math, Birmingham B15 2TT, W Midlands, England
  • 3 Univ Lyon, CNRS, UMR 5208, Inst Camille Jordan, F-69622 Villeurbanne, France
  • 4 INRIA Lyon Doua, INRIA Team Dracula, F-69603 Villeurbanne, France
  • 5 Peoples Friendship Univ Russia, RUDN Univ, 6 Miklukho Maklaya St, Moscow 117198, Russia
  • 6 IIT Kanpur, Dept Math & Stat, Kanpur 208016, Uttar Pradesh, India
Ключевые слова
population distribution; wealth distribution; population dynamics; long transients
Дата создания
20.07.2021
Дата изменения
20.07.2021
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/74567/
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