Autowave mathematical model of urban ecosystems with spatial inhomogeneities

A model of spatio-temporal self-organization of urban ecosystems as a superposition of conjugated active media, taking into account the nonuniformity of anthropogenic and natural factors. The high rate of growth of population and density due to the concentration of residential, industrial, commercial and other objects, as well as communication media, leads to a reduction of areas of natural biocenoses, autocatalysis of the development of anthropogenic processes and, consequently, an increase in the nonlinearity of system-wide processes. The model is based on the FitzHugh-Nagumo equation, modified by the authors. The validity of this type of application is determined by the relative simplicity of the system analysis of the two equations of the «activator - inhibitor» type. The conditions for the formation of an excitable / unexcited state of the active medium depending on the population density and the kinetic parameters of the system, as well as the formation of barrier zones such as tunneling and locking in the course of the structure formation of urban ecosystems are obtained. Analytic and numerical investigation of stationary solutions of the system is carried out.The dimensionless model is confirmed by the dynamics of population and population density and spatial data development of Moscow (Kuntsevo District) from 1952 to 1968. The model with spatial inhomogeneities allows to reveal threshold values of control parameters and to consider the basic principles of development of autowave processes forming the structure of urboecosystems. Keywords: urban ecosystem, self-organization, active medium, autowaves, heterogeneous structures