The application of a distributed model of active media for the analysis of urban ecosystems development

A. E. Sidorova ; N. T. Levashova ; A. E. Semina ; A. A. Melnikova

Matematičeskaâ biologiâ i bioinformatika, Tome 13 (2018) no. 2, pp. 454-465.

Résumé

A model of spatiotemporal self-organization of urban ecosystems as a superposition of conjugate active media that takes into account inhomogeneities of anthropogenic and natural factors is proposed. The type of ecosystems under assumption is characterized by a high rate of population growth and density due to the concentration of residential, industrial, commercial and other objects, as well as communication media. These conditions reduce the "buffer capacity" of natural subsystems and increase the nonlinearity and consequently the instability of system processes within the boundaries of urban ecosystems. The model is based on the system of FitzHugh-Nagumo equations, modified by the authors so to take into account inhomogeneities of anthropogenic (activator) and natural (inhibitor) factors. The validity of the application of an equation of this type is determined by the relative simplicity of the system analysis of two equations of the "activator-inhibitor" type. The previously published analytical studies of a system of equations of this type made it possible to create on its basis an adequate model for urban ecosystems development. The numerical solution of the system in the two-dimensional case was carried out in a rectangular region. On the boundaries of the domain the homogeneous Neumann conditions were given, the initial distribution was assumed to be known. The solution was carried out by the method of evolutionary factorization. The iterative process continued until complete stationing. The developed model is used for analysis and forecasting the development of the territory of New Moscow. The arrays of values of the control parameters of the model, which were subsequently taken into account in numerical implementation, were obtained on the basis of the aerial survey data and maps of the studied territories translated into digital form using the C++ authoring application, which allows to create text files with image-based data. The code was created in the OpenCL environment and implemented using AMD FIREPRO graphics processors. Graphical interpretation was carried out using the "Serfer" program.

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