UkrainianProfessional Education

Abstract

Currently, the phenomena of deterministic (Dynamic) chaos are widely used in science and technology. Therefore, now the urgent task is to study new phenomena and new manifestations of deterministic chaos. This paper examines a fundamentally new manifestation of deterministic chaos (Deterministic chaos of the second kind). In this regard, previously known manifestations of deterministic chaos should be called manifestations of chaos of the first kind (The previously known type of deterministic chaos, in our terminology, is chaos of the first kind). Deterministic chaos of the first kind is chaos that is directly related to the deterministic - chaotic behavior of the dynamic variables of a given dynamic system. At the same time, our work examines the characteristic features of deterministic chaos of the first kind and methods for generating such chaos. In our work, we considered a fundamentally different type of manifestation of dynamic chaos, namely deterministic chaos of the second kind. Deterministic chaos of the second kind is not directly related to the deterministic chaotic behavior of the dynamic variables of a dynamic system and can only exist in characteristics that are not directly related to the dynamic variables. That is, dynamic chaos of the second kind arises only in second-order manifestations: For example, in the Fourier spectrum. In a more general case, this could be any other type of spectrum (Not Fourier) and even another characteristic different from the spectrum. The paper provides two examples of deterministic chaos of the second kind. The work also proposes a general technique for generating time series demonstrating deterministic chaos of the second kind∗. It is very important that dynamic chaos in the examples given in this work manifests itself not in the time series themselves (Which are completely random) but in the Fourier spectrum of these time series. Thus, the original series itself (The original signal itself) can be random, but at the same time, the spectrum of this series, if considered as another time series, can exhibit deterministic chaotic behavior. Thus, for the first time we were able to build a bridge between completely random systems and deterministic chaotic systems. That is, in our work we were the first to show that the same system can be considered both random (From the point of view of the behavior of its variables) and at the same time as deterministic-chaotic (From the point of view of its spectrum or other similar characteristics). Goal of the work. Study of a newtype of deterministic chaos discovered by the authors (Deterministic chaos of the second kind) and the study of its properties and methods for generating this type of chaos

Keywords:

Deterministic chaos of the second kind, deterministic chaos in the spectrum, generating chaos of the second kind, bridge between completely random systems and deterministic chaotic systems, the same system can be considered both random (Behavior of its variables) and deterministic-chaotic (Its spectrum or other similar characteristics)