Why a Classification Based on Linear Approximation to Dynamical Systems Often Works Well in Nonlinear Cases

Authors

Julio Urenda, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

10-2019

Comments

Technical Report: UTEP-CS-19-103

Abstract

It can be proven that linear dynamical systems exhibit either stable behavior, or unstable behavior, or oscillatory behavior, or transitional behavior. Interesting, the same classification often applies to nonlinear dynamical systems as well. In this paper, we provide a possible explanation for this phenomenon, i.e., we explain why a classification based on linear approximation to dynamical systems often works well in nonlinear cases.