The Model of Structurization of Urban Ecosystems as the Process of Self-Organization in Active Media

Abstract

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. This type of ecosystems is characterized by a high rate of population growth and density due to the concentration of residential, industrial, commercial and other facilities, as well as means of communication. These conditions violate the dynamic equilibrium of energy, substance and information flows, reduce the “buffer capacity” of natural subsystems, increase the nonlinearity, and, as a consequence, instability of system processes. The model is based on the modified by the authors Fitz-Hugh-Nagumo equations, taking into account the inhomogeneities of the anthropogenic (activator) and natural (inhibitor) factors. The validity of the application of this type of equations is determined by the relative simplicity of the system analysis of two equations of the "activator-inhibitor" type. The conditions for the formation of an excitable/unexcitable state of the active medium and the initial burst of an autowave depending on the population density and the kinetic parameters of the system (activator and inhibitor), as well as the criteria for the formation of transition zones between cities, are obtained (based on calculations made from aerial photography). The obtained value of the dimensionless model population density in the region of the transition layer (the barrier on the path of the autowave front) and on the outskirts of residential arrays made it possible to reveal the proportionality coefficient between the parameters of the model problem and the corresponding values in a real urban environment. The dimensionless model is confirmed by data on population density and population density and Moscow map data from 1946 to 2014. The model makes it possible to identify threshold values of control parameters and to consider the basic principles of development of autowave processes forming the structures of urban ecosystems.