Abstract

The study of the problems of sustainable devel-opment of the ecological and urban planning system population ↔ environment of various levels of its functional and spatial integrity (lo-cal, regional, national, world-wide) reveals a number of fundamental provisions that estab-lish the conceptual foundations of a new direc-tion urban planning science that potentially exists certain individual works. The development of urban planning aspects of the stability theory is based on the funda-mental concept of the physico-mathematical stability theory that is more developed at the present and the research findings, which established the cyclical nature of the multilevel processes of wave development of the popula-tion ↔ environment system. The urban plan-ning stability theory studies the nature of the vi-brational development of urbanization process-es accelerating a multi-level ecological space. The paper reveals a number of similarities and fundamental differences the states of stability and the dynamic pattern that are inher-ent the development of living and inanimate natural systems. Regarding the differences state of equilibrium: equilibrium is the goal of development for living systems within a certain cycle and the level of their spatial integrity. For inanimate systems equilibrium is the initial state. Concerning the differences the stability of the location of the center of mass: the center of mass should occupy the highest possible position (in the range of ecological equilibrium) for living systems; for the inanimate-to take the lowest possible position. When developing the urban development aspects of stability theory were used such concepts of physical and mathematical stability theory as: asymptotic stability; stability in time according to Lyapunov; stability in space (stable − unstable node, stable − non-stable focus , stable center). Marked con-cepts are important for the analysis of multi-level processes of accelerating development of the ecological and urban planning system; fore-casting the direction of its further changes; de-termination of focuses and parameters of appli-cation of urban planning regulatory influences; adapted sustainable development management.

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