A distributed medium simulated FHN system describing the dynamics of objects of different nature - physical, chemical, biological, social, economic is considered. The analytical proof of the existence of solutions in the form of a travelling pulses of a complex profile. Such solutions can be used to describe a wide range of phenomena - from distribution of information, formation of shocks (such as vibration in the Earth's crust or the prices of financial assets, etc.) to the dynamics of socio-economic processes.
The work is devoted to the problem of constructing a smooth nonlinear stabilizing controller for a class of control systems, where the coefficients are weakly nonlinear functions of the state, resulting in the presence of the right-hand side of the equations of the dynamics of the so-called small parameter. An algorithm for designing the controller, allowing to build it into a numerical-analytical form, which significantly reduces the computational cost.
Linear nonstationary control systems with periodic interval constraints on the elements of a system matrix are considered. The sufficient conditions for their robust stability are established using the method pf comparison with the Luapunov vector function of a special type/They are shown to be not only sufficient, but also necessary conditions if additional constraints are introduced.
An approach to finding optimal trajectories for a class of problems of economic dynamics associated with turnpike theorems by using the singular perturbations theory methods. An algorithm for constructing uniform approximations of zero order for trajectories of balanced growth for the model that combines the properties of dynamical models of Leontief and Neumann. Constructed a numerical example.
A methodology is presented that allows to analyze and forecast dynamics of Russia’s foreign trade indicators published in balance of payments. Basing on the methodology, a model is constructed consisting of econometric and balance ratios. This model gives an opportunity to describe balance of payments variables with high accuracy. Model is adapted for midterm forecasting of monthly and quarterly data. With the help of the model discussed it is possible to simulate various economic scenarios and their influence on Russia’s economy.
The article describes mathematical analysis methods of distributions in multidimensional space of subject’s characteristics in social sciences. The necessity is motivated to take into account measure (frequency) and metric. Methods of metric reliability analysis for the general population are considered using (e, d)-sets (Shannon). As an example UN Human Development Data are analyzed.
A non-standard macroeconomic approach is discussed in this paper. An aggregate household rational behavior nonlinear dynamic model is presented, in which household is characterized by budget constraint with inclusion of various financial and investment instruments. Model is fully solved what means that final trajectories for consumption and labor are derived. A key feature of this paper is specific type of utility function that allows to estimate both consumption and labor trajectories.
The paper analyses the necessity of seasonal adjustment in dynamic models. It is shown, that seasonal adjustment of the time series can influence its’ properties in terms of unit root and cointegration tests. This influence depends of the seasonal adjustment procedure and the test selected. If there is a cointegration between series, seasonal adjustment of any type reduces the quality of estimates of parameters of cointegration equation if the seasonality in original series is such that there is no seasonality in cointegration equation. If seasonality is present in the cointegration equation, seasonal adjustment increases the quality of estimates and identification of the presence of cointegration.