Autowave Model of Megapolis Morphogenesis in the Context of Inhomogeneous Active Media

Sidorova, A. E.; Левашова, Н. Т.; Semina, A.E.

doi:10.3103/s1062873819010258

Cited by 6 publications

(1 citation statement)

References 8 publications

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“…In order to effectively apply the activator-inhibitor model for an adequate description of urban ecosystems, it is necessary to investigate thoroughly the reasons for their growth and the processes that inhibit this growth. While the density of the population and buildings is an obvious activator of urban ecosystem development, the inhibitor is determined by the policies determining urban planning and is different for each country [24,25]. Thus, any study should be preceded by the choice of an object and the determination of its individual characteristics.…”

Section: Methodsmentioning

confidence: 99%

A Spatio-Temporal Autowave Model of Shanghai Territory Development

et al. 2019

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A spatio-temporal model of megacity development that treats the megacity as an active medium is presented. From our point of view, it is advisable to consider the process of urban ecosystem development from the standpoint of the theory of autowave self-organization in active media. According to this concept, the urban ecosystem is considered as interacting with each other’s natural and anthropogenic subsystems with significant heterogeneity of areas affected by human intervention and urban geobiocoenoses. The model is based on the general principles of active medium dynamics; therefore, it is universal for any object to be considered an active medium. The only difference when using the model to predict the development of urban ecosystems in countries with different socio-economic and political prerequisites is the variety of parameters included in the model, i.e., the activation parameter, the autowave process inhibitors, and the characteristic scales of the activator and inhibitor. The model was tested on the example of Moscow expansion in the period of 1952–1968 and showed good agreement with the map data. By means of the model, a prediction of Shanghai and surrounding territory development until 2030 was made.

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Section: Methodsmentioning

confidence: 99%

A Spatio-Temporal Autowave Model of Shanghai Territory Development

et al. 2019

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Solving forward and inverse problems involving a nonlinear three-dimensional partial differential equation via asymptotic expansions

Chaikovskii,

Zhang

2023

IMA Journal of Applied Mathematics

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This paper concerns the use of asymptotic expansions for the efficient solving of forward and inverse problems involving a nonlinear singularly perturbed time-dependent reaction–diffusion–advection equation. By using an asymptotic expansion with the local coordinates in the transition-layer region, we prove the existence and uniqueness of a smooth solution with a sharp transition layer for a 3D partial differential equation. Moreover, with the help of asymptotic expansion, a simplified model is derived for the corresponding inverse source problem, which is close to the original inverse problem over the entire region except for a narrow transition layer. We show that such simplification does not reduce the accuracy of the inversion results when the measurement data contain noise. Based on this simpler inversion model, an asymptotic-expansion regularization algorithm is proposed for efficiently solving the inverse source problem in the 3D case. A model problem shows the feasibility of the proposed numerical approach.

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Stability of a stationary solution of a system of activator–inhibitor-type equations with a double-scale internal transition layer

Левашова

Samsonov

2023

Theor Math Phys

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Autowave Model of Megapolis Morphogenesis in the Context of Inhomogeneous Active Media

Cited by 6 publications

References 8 publications

A Spatio-Temporal Autowave Model of Shanghai Territory Development

A Spatio-Temporal Autowave Model of Shanghai Territory Development

Solving forward and inverse problems involving a nonlinear three-dimensional partial differential equation via asymptotic expansions

Stability of a stationary solution of a system of activator–inhibitor-type equations with a double-scale internal transition layer

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