An Algorithm for Decomposition Control and Prediction of Trajectories of Nonlinear Stochastic Systems Under Different-Speed Processes in Their Dynamics

The author proposes a decomposition algorithm for predicting the trajectories of nonlinear stochastic systems whose dynamics contain subprocesses significantly different in speed. The algorithm is focused on reducing the time to obtain predictive results for substantially nonlinear objects and systems, when calculations based on their complete mathematical models are associated with a large amount of computation and the complexity of temporary adjustment of parameters.

     

Using Algorithms of Decomposition for Computation of Linear Stochastic Models

The mathematical apparatus of decomposition is used to solve the problem of analysis and computation of stiff stochastic systems of differential equations. A theorem substantiating the adequacy of a solution obtained is formulated and an algorithm of computation of stiff stochastic systems by the method of depression of equations is given.     

Modeling the Control Effects of the Banking System on the Functioning of the Economy. III. Calculation and Decomposition of Models with a Stepped Boundary Layer*

Cybernetics and Systems Analysis - A mathematical formalism is proposed for calculating mathematical models of financial and economic systems (FES) and determining the optimal values of control...     

State estimation and filtering in stochastic systems using adequate simplification

The method of order reduction in solving stochastic problems of state estimation and filtering is considered. The method presented concerns the case where mathematical models of objects being studied are defined by systems of nonstationary differential equations. Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 98–102, September–October, 1999.     

Determining the number of fast and slow components in decomposition of arbitrarily large linear dynamical models

A new numerical method is proposed for determining the real parts of the eigenvalues of ill-conditioned matrices of arbitrary size. Convergence of the numerical algorithm is proved.Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 3–9, November–December, 1991.     

Convergence of Algorithms of the Order Reduction Method in Analysis of Nonlinear Mathematical Models of Fragments of Automatic Control Systems and Process Control Systems

A theorem determining adequacy conditions for reduction of dimension in a specified class of mathematical models of nonlinear dynamic systems is formulated and proved.     

Mathematical Modeling of the Dynamics of Crisis Situations and Optimization of Capital Relocation Market Management in the Context of Globalization in the World Financial and Economic System

The article continues a series of studies analyzing the features of capital relocation (movement) and mathematical modeling of the dynamics of the world financial and economic system (FES) in the context of globalization. Structuring features of capital transfer processes in the context of a modern globalized FES and their impact on the efficiency of the investment portfolio and the economy of donor and recipient countries are considered. The relationship between the dynamic processes of the movement of borrowed capital and the Buffett indicator is established as a characteristic feature of the emergence and development of crises. The conditions have been determined whereby further capital injection, i.e., “flooding the crisis with money,” ceases to be effective.

     

Mathematical Modeling of the Effect of “Splashing out” and Optimization of Management of Banking and Economic Systems Under Globalization Conditions

The problem of mathematical modeling of the “splashing out” effect is considered. The existence of this phenomenon was observed some time ago by specialists-practitioners who were forced to make management decisions affecting the dynamics of banking and economic systems. The influence of this effect as one of important new phenomena must be taken into account in decision support systems of new generation. A mathematical definition of the coefficient of globalization of the world banking system is formulated.