We Can Always Reduce a Non-Linear Dynamical System to Linear -- at Least Locally -- But Does It Help?

Authors

Orsolya Csiszar, Aalen UniversityFollow
Gábor Csiszar, Óbuda UniversityFollow
Olga Kosheleva, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow
Nguyen Hoang Phuong, Thang Long UniversityFollow

Publication Date

7-1-2023

Comments

Technical Report: UTEP-CS-23-41

Abstract

Many real-life phenomena are described by dynamical systems. Sometimes, these dynamical systems are linear. For such systems, solutions are well known. In some cases, it is possible to transform a nonlinear system into a linear one by appropriately transforming its variables, and this helps to solve the original nonlinear system. For other nonlinear systems -- even for the simplest ones -- such transformation is not known. A natural question is: which nonlinear systems allow such transformations? In this paper, we show that we can always reduce a nonlinear system to a linear one -- but, in general, it does not help, since the complexity of finding such a reduction is exactly the same as the complexity of solving the original nonlinear system.