Overview
- 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
Part of the book series: Nonlinear Systems and Complexity (NSCH, volume 27)
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Table of contents (14 chapters)
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Front Matter
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Back Matter
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
- ordinary differential equations
About this book
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 asspecialists 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.
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Almost Periodicity, Chaos, and Asymptotic Equivalence
Authors: Marat Akhmet
Series Title: Nonlinear Systems and Complexity
DOI: https://doi.org/10.1007/978-3-030-20572-0
Publisher: Springer Cham
eBook Packages: Engineering, Engineering (R0)
Copyright Information: Springer Nature Switzerland AG 2020
Hardcover ISBN: 978-3-030-19916-6Published: 04 November 2019
eBook ISBN: 978-3-030-20572-0Published: 20 June 2019
Series ISSN: 2195-9994
Series E-ISSN: 2196-0003
Edition Number: 1
Number of Pages: XVII, 360
Number of Illustrations: 1 b/w illustrations, 25 illustrations in colour
Topics: Mathematical and Computational Engineering, Applications of Nonlinear Dynamics and Chaos Theory, Ordinary Differential Equations, Mathematical Models of Cognitive Processes and Neural Networks