Pham / Volos / Kapitaniak Systems with Hidden Attractors

From Theory to Realization in Circuits
1. Auflage 2017
ISBN: 978-3-319-53721-4
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 111 Seiten, eBook

Reihe: SpringerBriefs in Applied Sciences and Technology

This brief provides a general overview of nonlinear systems that exhibit hidden-attractor behavior, a topic of interest in subjects as divers as physics, mechanics, electronics and secure communications. The brief is intended for readers who want to understand the concepts of the hidden attractor and hidden-attractor systems and to implement such systems experimentally using common electronic components. Emergent topics in circuit implementation of systems with hidden attractors are included. The brief serves as an up-to-date reference on an important research topic for undergraduate/graduate students, laboratory researchers and lecturers in various areas of engineering and physics.

Zielgruppe

Research

Autoren/Hrsg.

Pham, Viet-Thanh

Volos, Christos

Kapitaniak, Tomasz

Inhaltsverzeichnis

1;Preface;6
2;Contents;8
3;1 Introduction;11
3.1;1.1 Self-Excited Attractors;11
3.2;1.2 Hidden Oscillations;14
3.3;1.3 Localization of Hidden Attractors;17
3.4;1.4 Control and Synchronization;17
3.5;1.5 Hidden Oscillations in Applied Models;19
3.5.1;1.5.1 Phase-Locked Loop Circuits;19
3.5.2;1.5.2 Automatic Control Systems;20
3.5.3;1.5.3 Chua's Circuit Oscillator;20
3.5.4;1.5.4 Electromechanical Systems;20
3.6;1.6 Families of Systems with Hidden Attractors;21
3.6.1;1.6.1 Systems Without Equilibrium;21
3.6.2;1.6.2 Systems with Stable Equilibrium;22
3.6.3;1.6.3 Systems with an Infinite Number of Equilibria;22
3.7;References;23
4;2 Systems with Stable Equilibria;30
4.1;2.1 Wang--Chen System with Only One Stable Equilibrium;30
4.2;2.2 Simple Flows with One Stable Equilibrium;32
4.3;2.3 Systems with Stable Equilibrium Points;35
4.4;2.4 Constructing a System with One Stable Equilibrium;38
4.5;2.5 Double-Scroll Attractors in Systems with Stable Equilibria;40
4.6;2.6 Fractional-Order Form of a System with Stable Equilibrium;41
4.7;References;43
5;3 Systems with an Infinite Number of Equilibrium Points;45
5.1;3.1 Simple Systems with Line Equilibrium;45
5.2;3.2 Systems with Closed Curve Equilibrium;48
5.3;3.3 Systems with Open Curve Equilibrium;52
5.4;3.4 Constructing a System with Infinite Equilibria;54
5.5;3.5 Multi-scroll Attractors in a System with Infinite Equilibria;55
5.6;3.6 Fractional-Order Form of Systems with Infinite Equilibria;56
5.7;References;57
6;4 Systems Without Equilibrium;59
6.1;4.1 Sprott A (Nose--Hoover) System;59
6.2;4.2 Wei System Without Equilibrium;60
6.3;4.3 Simple Systems with No Equilibrium;61
6.4;4.4 Constructing a System with No Equilibrium;64
6.5;4.5 Multi-scroll and Multi-wing Attractors in Systems Without Equilibrium;67
6.6;4.6 Fractional-Order Form of Systems Without Equilibrium;69
6.7;References;70
7;5 Synchronization of Systems with Hidden Attractors;72
7.1;5.1 Synchronization via Diffusion Coupling;72
7.1.1;5.1.1 Diffusion Coupling of Two Systems with One Stable Equilibrium;72
7.1.2;5.1.2 Diffusion Coupling of Two Systems with Infinite Equilibria;73
7.1.3;5.1.3 Diffusion Coupling of Two Systems Without Equilibrium;74
7.2;5.2 Synchronization via Nonlinear Control;75
7.2.1;5.2.1 Synchronization of Systems with One Stable Equilibrium;76
7.2.2;5.2.2 Synchronization of Systems with Infinite Equilibrium;78
7.2.3;5.2.3 Synchronization of Systems Without Equilibrium;81
7.3;References;83
8;6 Circuitry Realization;85
8.1;6.1 Basic Electronic Components and Electronic Circuits;85
8.2;6.2 Circuit Implementation of a System with One Stable Equilibrium;89
8.3;6.3 Circuit Implementations of Systems with Infinite Equilibria;92
8.3.1;6.3.1 Circuit Implementation of a System with Line Equilibrium;92
8.3.2;6.3.2 Circuit Implementation of a System with Closed Curve Equilibrium;95
8.3.3;6.3.3 Circuit Implementation of a System with Open Curve Equilibrium;98
8.4;6.4 Circuit Implementation of a System Without Equilibrium;101
8.5;6.5 Circuit Implementation of a System with Different Families of Hidden Attractors;104
8.6;References;107
9;7 Concluding Remarks;109
9.1;References;110
10;Index;111

Über Autor(innen)

Viet-Thanh Pham graduated in Electronics and Telecommunications in 2005 at Hanoi University of Technology, Vietnam. He received the PhD degree in Electronics, Automation, and Control of Complex Systems Engineering in 2013 from the University of Catania, Italy. Currently, he is Lecture at the School of Electronics and Telecommunications, Hanoi University of Science and Technology, Vietnam, where he has been involved in projects concerning the study of nonlinear circuits and systems. His scientific interest includes applications of nonlinear systems, analysis and design of analog circuits, and FPGA-based digital circuits.

Dr. Volos received his Physics Diploma, his M.Sc. in Electronics and his Ph.D. in Chaotic Electronics, all from the Aristotle University of Thessaloniki. He currently serves as an Assistant Professor in the Physics Department of the Aristotle University of Thessaloniki. His research interests include, among others, the design of chaotic electronic circuits and their applications.

Professor Kapitaniak is Head of Division of Dynamics, Technical University of Lodz. He is the corresponding member of the Polish Academy of Sciences.