Interchangeability Conditions for Autonomous Processes Models in Finite-dimensional and Infinite-dimensional Spaces

Abstract

The paper presents the interchangeability conditions for the finite-dimensional, infinite-dimensional, and discrete models of dynamics of autonomous processes and, using the one-dimensional processes as an example, shows that with the certain ratio of the model parameters and appropriate choice of initial functions these conditions are satisfied. Reveals how, subject to the conditions of interchangeability, the process generated by an ordinary differential equation can be represented in the functional space by the trajectory of a discrete dynamic system.Considers dynamic models in the class of ordinary differential equations and delay differential ones. Since the solution spaces of such equations are, in general, different: a finite-dimensional arithmetic space for solutions of the ordinary differential equation and the infinite-dimensional functional space for solutions of the delay differential equation, the problem to reduce dynamic models to the uniform form is associated with representation of processes in both types of spaces. Based on the interchangeability mechanisms of dynamic models of the process under study, the paper proposes methods to reduce the models of dynamics to a uniform form.The results are verified by direct calculations using the specific examples. Interchangeability is used to compare the oppositely directed processes represented by different types of dynamic models. To compare one-dimensional multidirectional processes, presented by dynamic models of various types and having a different behavior pattern, examples of the error models are given. An accuracy of the comparison model of delay type is illustrated by a numerical simulation example.