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American Journal of Applied Science and Technology

Peer Reviewed | Open Access | E-ISSN: 2771-2745
Published Article

Basic Concepts of Dynamical Systems and Their Analysis in Examples

Basic Concepts of Dynamical Systems and Their Analysis in Examples

Authors

  • Solayeva Mehribon Norimonovna
    University of World Economy and Diplomacy, Senior Lecturer, Department of "Systematic Analysis and Mathematical Modeling", Uzbekistan

DOI:

https://doi.org/10.37547/ajast/Volume06Issue04-14

Keywords:

Dynamical system iteration orbit of an initial point

Abstract

This article provides an introduction to the concept of dynamical systems and explores several fundamental notions, such as iterative processes, the orbit of an initial point, and fixed points. Along with theoretical definitions, a detailed analysis of these concepts is presented through various examples. Furthermore, to facilitate the learning process for undergraduate and graduate students entering the field of dynamical systems, each foundational concept is thoroughly explained using illustrative examples.

References

Devaney, Robert L., A first course in chaotic dynamical systems: theory and experiment 1992

Rozikov U. A., Solaeva M.N., Behavior of trajectories of a quadratic operator splitted to uncountable linear operators. {it Lobachevskii Journal of Mathematics.} 2023, Vol. 44, No. 7, p. 2910-2915.