This paper studies the problem of safe and sustainable progressive socio-economic and energy development of Russian regions in terms of reforming economy. In this study, the fractal approach in the framework of nonlinear dynamics for a number of indicators was used, as well as a technique of analysis and behavior forecasting of time series of economic systems at the regional level. The authors have performed forecasting works on energy-investment attractiveness of the subjects of the Ural region up to 2020. The calculations were performed for three scenarios of socio-economic development of regions, which will allow prioritizing the regional energy development and suggesting areas of efficient use of financial, material and energy resources.Consideration of the obtained results will allow governmental bodies to pursue a more balanced policy and allow business entities to identify priority solutions on the enhancement of the investment process in the energy of considered regions.

This paper reviews main approaches to risk assessment. The authors accented attention on the nonlinear approach to the theory of risks. It is proposed to define economic risk as the probability of threats that could have material adverse effect on the economic system under study and to change its current state. The method and the program product designed by the authors integrate a wide range of indicators of economic and financial activities at the regional level in the program-technical complex. This paper describes a new method for assessing synergistic and prediction of risk over long time rows of economic indicators at the regional level, including methods of nonlinear and chaotic dynamics, enabling a pseudo-phase and phase portraits, to determine the volatility, to calculate fractal characteristics and predict the behavior of socio-economic indicators with modernized method of Hurst, to model based on recovery probability distribution function of nonequilibrium potential function, to determine the local and global stability of the regional economy and to identify risks as the probability of the threats of an economic nature.

In the article, a synergetic method of the economic time series forecasting on the basis of the modified method of Hurst is discussed. It is a new nonlinear method of predicting the development of economic systems according to time series on macro- and mesolevels. The main theorem underlying the forecasting method is formulated and strictly proved: for a chaotic series of a particular length it is possible to specify a time interval where the series is reliably predicted with the Hurst exponent more than 0.5. The examples of the fractal characteristics’ calculation and the forecasting taking into account time of reliable forecast of the socioeconomic indexes’ behavior — oil prices, natural gas prices, the Dow Jones index, the «euro-dollar» prices, the Gross Domestic Product, and some other indicators at the regional level are given. All calculations are carried out by means of the specialized software product upgraded for the task solution set in this article.

Methodical questions of diagnosing drug situation in the territory. It shows the composition of performance indicators to assess the state of the drugs situation in the regions. The approaches to the determination of the key indicators of the drug situation - the actual number of drug users, a critical mass of drug addicts, the damage caused by drug addiction. Given the results of the diagnosis of the drug situation for Urals Federal District for the period 1999 - 2003 years. The main directions of work to counter the spread of drug addiction and neutralize its effects within the county.

In the article, the contemporary issues of the reproduction of the Russian population, their reasons, and state policy toward them are considered. Relevance of the task solution of assessment of the most expected birth rate dynamics of the Russian population in future in the conditions of low norms of the parenthood status taking into account the influence of government measures for the birth rate stimulation is proved. In order to achieve this objective, on the basis of the behavior probability distribution function of crude birth rate, the probabilistic assessment of the future birth rate dynamics of the Russian population was conducted. On the basis of the modernized Hirst method, two expected dynamics trajectories of crude birth rate were constructed: the first trajectory corresponds to the scenario at which the value of crude birth rate will be in the range of 8-10,5 born / 1000 people (probability — 0,182), including the negative external impact, the second trajectory will be in the range of 13-16,5 born / 1000 people (probability — 0,618), including the positive external impact. In spite of the fact that these scenarios are quite different, the dynamics trajectories of crude birth rate predicted according to them during the period of 2015-2041 that corresponds to the time of the reliable prediction are almost identical. The analysis of the received results enabled to conclude that the state population policy cannot affect the future dynamics of the birth rate due mainly to to the conjunctural changes.These conclusions confirm the intellectual vested interest of the academic circles that government regulation of a demographic situation in Russia has to be aimed, first of all, at the health improvement and increase of the expected life interval of the population.

In the article, the approach based on the authors’ hypothesis is considered: the development of Russia has specific characteristics (on the one hand, its size, mentality and certain closed nature of its economy, on the other hand, the considerable dominating resource and human potential, and, as the result, its real role in the world economic community). The diagnostics of these characteristics (at the level of the individual’s welfare and territory of accommodation) reveals crises, estimates threats to region socio-economic development at early stages and helps to evaluate the state of a region for 3-5 years. In other words, managers have time necessary for rapid response to the crisis phenomena and administrative mistakes, for decreasing the impact of the arising threats. The purpose of the article is to present the theoretical and methodological tools of the appearing threats recognition at their early stages, which allows to enter the crisis period with smaller losses. Computational experiments to classify the prior socio-economic crises have been conducted (9 possible options are considered), the trajectories of change of the main indicators of the individual’s welfare and territory of residence influenced by various factors are digitized. On the basis of the proposed approach (named as the economic tomography), the attempt of the comprehensive assessment of the state of Russian typical representative regions is made.