Polysystem methodology elaborated for comprehensive analysis of geographical objects considers them as interrelated systems of different types. Each systematic interpretation of a territorial object is formed as a theory describing this object with a special language used for construction of a certain type of models. This paper proposes new methods to develop geographical models and describes several types of systematic models constructed by these methods.

This paper suggests models of the landscape complexes based on the theory of complex systems and category-functorial approach. With the use of the space Landsat images the existence of the Earth's landscape field is proved and criteria of its parameter characterization is suggested. The unity of spatiotemporal changes of the landscape units is substantiated.

The model of geographical space of the Earth is represented as a multilevel discrete grid structure. This provides a scientific basis for the construction of a natural geoinformation system of the globe with invariant organization of data in the form of a universal grid, i.e. a different-level set of elementary cells with discrete topology. A grid structure is a multilevel system of reference points, with respect to which a spatial analysis of the territory is carried out. Reference points have attributes reflecting the territorys hierarchic level and location characteristics. It is found that there is a connection between the topology of the cells and specific structures of the Earth, and between the lineament network and the hydrological network in particular.

A spatial and temporal diversity of processes and phenomena is observed in mountaintaiga landscapes as the object of management. A knowledge of the mechanisms of their interactions makes it possible to effectively manage these processes and phenomena. The methodology of system analysis and mathematical models of interaction mechanisms are used in the analysis of these phenomena. A visualization of modelling results is carried out using geoinformation mapping methods.

We examine the theoretical and applications-specific issues relating to modeling the temporal and spatial dynamics of forest ecosystems, based on the principles of investigating dynamical models. When developing the predictive dynamical models of forest resources, there is a possibility of achieving uniqueness of the solutions to equations by taking into account the initial and boundary conditions of the solution, and the conditions of the geographical environment. We present the results of a computer modeling and predictive mapping for the regional and subregional model of the forest resource dynamics.

Mathematical modeling provides a particularly important tool for studying the stream runoff formation processes, and its role is enhanced in the case of a sparse, obsolete monitoring network characteristic of most regions of Siberia. When analyzing spatio-temporal regularities of the water and sediment runoff in river systems, serious problems are caused by lack of the basic hydrological model capable of handling real-time data of hydrological measurements.
Calculations of unsteady flows in stream channels draw heavily on one-dimensional numerical models which are relatively easy to use and yield reliable results. Numerical investigations into the hydraulic regime of natural streams involve specific difficulties caused by the presence of nonlinear frictional forces in a turbulent flow, a variability in the channel geometry, the braiding of flows, the presence of floodplain depressions, riffles, etc. For especially complex stretches of rivers, a onedimensional approximation no longer fits the reality sufficiently adequately, so that the planar flow structure must be taken into account. For this purpose Saint Vennant's plane system of equations was used as the basis in order to develop further the numerical model due to this author which is intended for calculating the flow field, flow rates, levels, and impurity concentrations in natural water bodies of an arbitrary configuration or in a part of them. Fundamental laws of fluid mechanics are used as the basis for the model.
Spatial modeling of flows in complex regions necessitates reliable, consistent methods providing acceptable accuracy. As far as hydrological problems are concerned, the control volume method that allows the use of curvilinear grids was found to be the most powerful tool for obtaining the initial finite-difference relations.
This paper offers a number of examples illustrating the capabilities of the planar model for streams which is intended to resolve real problems arising at the design, construction and operation stages of engineering structures in river channels and floodplains.

The paper is devoted to mathematical modelling and numerical computations of a nonstationary free boundary problem. The model is based on processes of molecular diffusion of some products of chemical decomposition of a solid organic substance concentrated in bottom sediments. It takes into account non-stationary multi-component and multi-stage chemical decomposition of organic substances and the processes of sorption desorption under aerobic and anaerobic conditions. Such a model allows one to obtain quantitative estimates of incoming solute organic substances of anthropogenic origin having different molecular weights from the bottom sediments into water and to study the influence of seasonal variations of the concentration of solute oxygen in the near-bottom water on the direction of exchange processes in the system “waterbottom”.
Identification of parameters of the mathematical model with the use of experimental data and with the employment of a priori information of the model's structure is carried out. Comparison of the numerical simulations with experimental data is conducted to the end of verification of efficiency and plausibility of the proposed mathematical model of secondary pollution. It implies assessment of water quality on account of the processes of exchange in the system “waterbottom”. The results of computations of non-stationary fluxes at the boundary “waterbottom” are analyzed. A model example is used to estimate the potentials of the biogenic load on the water reservoir.

The flow trough the Strait of Gibraltar could be analyzed as a problem of two-layer hydraulic exchange between the Atlantic ocean and the Mediterranean sea. The shallow water equations in both layers coupled together are an important tool to simulate this phenomenon. In this paper we perform an upwind schemes for hyperbolic equations based on the Roe approximate Riemann solver, to study the resulting model. The main goal assigned was to predict the location of the interface between the two layers. Therefore the computational results obtained are compared to previous results and experiments.

In this work we deal with the design of the robust feedback control of wastewater treatment system, namely the activated sludge process. This problem is formulated by a nonlinear ordinary differential system. On one hand, we develop a robust analysis when the specific growth function of the bacterium μ is not well known. On the other hand, when also the substrate concentration in the feed stream sin is unknown, we provide an observer of system and propose a design of robust feedback control in term of recycle rate, in order to keep the pollutant concentration lower than an allowed maximum level sd.

The paper considers a methodology of mathematical modeling of ecological-economic processes at the regional level. The basis of the model is formed by equations, which describe two interacting blocks: economic and ecological ones. Equations of the economic block are represented by relations of generalized inter-branch balance, while the ecological part is described in terms of differential equations with deviations with respect to some given state of natural resources. Issues of i) information support of the model, ii) techniques used for identification of the coefficients, iii) scenario analysis and iv) forecasting are analyzed.

This paper is concerned with the methods of mathematical modeling of the socio-economic development of regions. The objective of this study is to analyze and assess the socio-economic potential of the territory having regard to its individual socio-economic and economic-geographical characteristics. The territory's individual characteristics, in turn, are treated as invariant conditions of its development. The study territory includes regions and federal districts of the Russian Federation.
An assessment of the regions' development potential is made from the perspective of analyzing their current socio-economic situation for the time interval 1999-2002 taken from official statistical handbooks. To accomplish this, a special-purpose mathematical model is developed in the form of a hierarchical fractal indicative function relating the generalized indicator characterizing the regions' development potential, or the “indicated” (that which is indicated versus indicator), to the particular socio-economic characteristics of the territory, or the development indicators of the local economy, via the model coefficients which is termed regulators.
As a result, the economic-mathematical model is generated in the form of an indicative function characterizing the current socio-economic situation of the regions and federal districts of Russia on different levels of economic organization (from local and regional to national). It reflects appropriately and dramatically the specific character of the region's socio-economic potential by the example of the connection of investments with the volumes of production. The model permits the position of the regions and districts to be identified in the system of inter-regional and national socio-economic links and economic-geographical conditions of development. The results derived from modeling the socio-economic development potential of Russia's regions have been used to construct the control surface of the country's economy characterizing the changes in the development potential of the federal districts toward its decrease.