Variation Approach and Principle of Maximum in Theory of Dynamic Systems

Abstract

The article shows dynamics of value figures on market of digital finance assets. The research studies methods of the sensitivity theory in tasks of optimal management of non-linear systems for automated monitoring and controlling the portfolio of digital finance assets and crypto-currencies. The authors study process modeling in economic systems, set the task of optimal management by the system of non-linear differential equations and target functionality, describe the variation method of task resolving, the principle of invariability of non-linear systems and possibilities to model economic systems provided by the solution. The approach to investigating dynamics of economic systems based on the principle of maximum was analyzed. The article shows possible application of the approach for resolving optimization tasks and for methods of management with split and continuous character in conditions of uncertainty typical of economic systems. Functions of non-linear sensitivity are identified. The use of the sensitivity theory for tasks of optimal management of non-linear systems was studied, illustrated by estimating the vector of unknown parameters of dynamic system. The authors analyze the condition in tasks of economic modeling with regard to uncertainty caused by social and psychological reasons. The material provided in the article shows possibilities of using the method of sensitivity analysis for tasks of system decomposition and related transformations in systems of differential equations.

Keywords

• mathematic models
• non-linear systems
• digital finance assets
• modeling economic processes