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Almost Periodicity, Chaos, and Asymptotic Equivalence

  • Marat Akhmet
Book

Part of the Nonlinear Systems and Complexity book series (NSCH, volume 27)

About this book

Introduction

The central subject of this book is Almost Periodic Oscillations, the most common oscillations in applications and the most intricate for mathematical analysis.  Prof. Akhmet's lucid and rigorous examination proves these oscillations are a "regular" component of chaotic attractors. The book focuses on almost periodic functions, first of all, as Stable (asymptotically) solutions of differential equations of different types, presumably discontinuous; and, secondly, as non-isolated oscillations in chaotic sets. Finally, the author proves the existence of Almost Periodic Oscillations (asymptotic and bi-asymptotic) by asymptotic equivalence between systems. The book brings readers' attention to contemporary methods for considering oscillations as well as to methods with strong potential for study of chaos in the future. Providing three powerful instruments for mathematical research of oscillations where dynamics are observable and applied, the book is ideal for engineers as well as specialists in electronics, computer sciences, robotics, neural networks, artificial networks, and biology.

  • Distinctively combines results and methods of the theory of differential equations with thorough investigation of chaotic dynamics with almost periodic ingredients;
  • Provides all necessary mathematical basics in their most developed form, negating the need for any additional sources for readers to start work in the area;
  • Presents a unique method of investigation of discontinuous almost periodic solutions in its unified form, employed to differential equations with different types of discontinuity;
  • Develops the equivalence method to its ultimate effective state such that most important theoretical problems and practical applications can be analyzed by the method.

Keywords

Chaos Li-Yorke Chaos Almost Periodic Solutions Discontinuous Almost Periodic Solutions Asymptotic Equivalence Impulsive Differential Equations Differential Equations with Piecewise Constant Argument Dynamics on Time Scales Bohr-Wexler Almost Periodic Functions Bohner-Wexler Almost Periodic Functions Neural Networks Almost periodic oscillations

Authors and affiliations

  • Marat Akhmet
    • 1
  1. 1.Department of MathematicsMiddle East Technical UniversityAnkaraTurkey

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-20572-0
  • Copyright Information Springer Nature Switzerland AG 2020
  • Publisher Name Springer, Cham
  • eBook Packages Engineering
  • Print ISBN 978-3-030-19916-6
  • Online ISBN 978-3-030-20572-0
  • Series Print ISSN 2195-9994
  • Series Online ISSN 2196-0003
  • Buy this book on publisher's site