Strongly unpredictable solutions of difference equations

Abstract

The theory of difference equations has wide application for approximation of differential operators, for constructing various discrete models, etc. Their usefulness is confirmed by numerous scientific publications, articles, and many international conferences. This article discusses new types of oscillations, unpredictable sequences, the presence of which shows the existence of chaos. The existence and uniqueness of strongly unpredictable solutions of non-linear difference equations are proved. An example with numerical simulations is presented to illustrate the theoretical results. The theory of difference equations has wide application for approximation of differential operators, for constructing various discrete models, etc. Their usefulness is confirmed by numerous scientific publications, articles, and many international conferences. This article discusses new types of oscillations, unpredictable sequences, the presence of which shows the existence of chaos. The existence and uniqueness of strongly unpredictable solutions of non-linear difference equations are proved. An example with numerical simulations is presented to illustrate the theoretical results.