This paper presents a method for modeling of real macroworld cyclic processes by the solutions of two (or more) linear differential equations with constant coefficients. It is shown that possible to send such model from any initial condition (point in phase space) to a prescribed final point in phase space for a prescribed amount of steps. As a result, conditions for a constructing closed cycle in phase space of any dimension were found. Switching from one system of equations to another is obtained then integral curve reaches some threshold — frontier in phase sheet (space). The analysis of convergence rate of the solution for such closed cycles is made. The integral curve behavior significant dependence of initial condition was shown.The obtained model is connected with experimental data in the form of time series and approximates them with solution of linear differential equations on condition of minimizing the RMS deviation. Proposed model also can be applied to a task of some index (technical, economical) reaching the prescribed meaning to a prescribed moment.
Смирнов В.Ю., Кузнецова А.В. О моделировании циклических процессов решениями кусочно-линейных разностных уравнений с постоянными коэффициентами по экспериментальным данным в виде временных рядов. Математическое моделирование и численные методы, 2022, № 4, с. 63–80.