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E-raamat: Systems with Hidden Attractors: From Theory to Realization in Circuits

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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.

Arvustused

This book is a concise reference in nonlinear systems with hidden attractors. Furthermore, emergent topics in circuit implementation of systems with hidden attractors are presented. This book can be used as a part of the bibliography in courses related to dynamical systems and their applications, nonlinear circuits, or oscillations in mechanical systems. (Kazuhiro Sakai, zbMATH 1387.37003, 2018) This book presents a state-of-the-art review of systems of this kind that have been found in the last few years. this is a book for researchers interested in an introduction to a promising field of research that can be read quickly and easily. (Jesús M. Gonzá1ez-Miranda, Mathematical Reviews, October, 2017)

1 Introduction
1(20)
1.1 Self-Excited Attractors
1(3)
1.2 Hidden Oscillations
4(3)
1.3 Localization of Hidden Attractors
7(1)
1.4 Control and Synchronization
7(2)
1.5 Hidden Oscillations in Applied Models
9(2)
1.5.1 Phase-Locked Loop Circuits
9(1)
1.5.2 Automatic Control Systems
10(1)
1.5.3 Chua's Circuit Oscillator
10(1)
1.5.4 Electromechanical Systems
10(1)
1.6 Families of Systems with Hidden Attractors
11(10)
1.6.1 Systems Without Equilibrium
11(1)
1.6.2 Systems with Stable Equilibrium
12(1)
1.6.3 Systems with an Infinite Number of Equilibria
12(1)
References
13(8)
2 Systems with Stable Equilibria
21(16)
2.1 Wang--Chen System with Only One Stable Equilibrium
21(2)
2.2 Simple Flows with One Stable Equilibrium
23(3)
2.3 Systems with Stable Equilibrium Points
26(3)
2.4 Constructing a System with One Stable Equilibrium
29(2)
2.5 Double-Scroll Attractors in Systems with Stable Equilibria
31(1)
2.6 Fractional-Order Form of a System with Stable Equilibrium
32(5)
References
34(3)
3 Systems with an Infinite Number of Equilibrium Points
37(14)
3.1 Simple Systems with Line Equilibrium
37(3)
3.2 Systems with Closed Curve Equilibrium
40(4)
3.3 Systems with Open Curve Equilibrium
44(2)
3.4 Constructing a System with Infinite Equilibria
46(1)
3.5 Multi-scroll Attractors in a System with Infinite Equilibria
47(1)
3.6 Fractional-Order Form of Systems with Infinite Equilibria
48(3)
References
49(2)
4 Systems Without Equilibrium
51(14)
4.1 Sprott A (Nose--Hoover) System
51(1)
4.2 Wei System Without Equilibrium
52(1)
4.3 Simple Systems with No Equilibrium
53(3)
4.4 Constructing a System with No Equilibrium
56(3)
4.5 Multi-scroll and Multi-wing Attractors in Systems Without Equilibrium
59(2)
4.6 Fractional-Order Form of Systems Without Equilibrium
61(4)
References
62(3)
5 Synchronization of Systems with Hidden Attractors
65(14)
5.1 Synchronization via Diffusion Coupling
65(3)
5.1.1 Diffusion Coupling of Two Systems with One Stable Equilibrium
65(1)
5.1.2 Diffusion Coupling of Two Systems with Infinite Equilibria
66(1)
5.1.3 Diffusion Coupling of Two Systems Without Equilibrium
67(1)
5.2 Synchronization via Nonlinear Control
68(11)
5.2.1 Synchronization of Systems with One Stable Equilibrium
69(2)
5.2.2 Synchronization of Systems with Infinite Equilibrium
71(3)
5.2.3 Synchronization of Systems Without Equilibrium
74(2)
References
76(3)
6 Circuitry Realization
79(24)
6.1 Basic Electronic Components and Electronic Circuits
79(4)
6.2 Circuit Implementation of a System with One Stable Equilibrium
83(3)
6.3 Circuit Implementations of Systems with Infinite Equilibria
86(9)
6.3.1 Circuit Implementation of a System with Line Equilibrium
86(3)
6.3.2 Circuit Implementation of a System with Closed Curve Equilibrium
89(3)
6.3.3 Circuit Implementation of a System with Open Curve Equilibrium
92(3)
6.4 Circuit Implementation of a System Without Equilibrium
95(3)
6.5 Circuit Implementation of a System with Different Families of Hidden Attractors
98(5)
References
101(2)
7 Concluding Remarks
103(2)
References
104(1)
Index 105
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.
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