Essentials of Nonlinear Circuit Dynamics with MATLAB® and Laboratory Experiments: 1st Edition (Hardback) book cover

Essentials of Nonlinear Circuit Dynamics with MATLAB® and Laboratory Experiments

1st Edition

By Arturo Buscarino, Luigi Fortuna, Mattia Frasca

CRC Press

289 pages

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Hardback: 9781138198135
pub: 2017-04-10
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This book deals with nonlinear dynamics of electronic circuits, which could be used in robot control, secure communications, sensors and synchronized networks. The genesis of the content is related to a course on complex adaptive systems that has been held at the University of Catania since 2005. The efforts are devoted in order to emulate with nonlinear electronic circuits nonlinear dynamics. Step-by-step methods show the essential concepts of complex systems by using the Varela diagrams and accompanying MATLAB® exercises to reinforce new information. Special attention has been devoted to chaotic systems and networks of chaotic circuits by exploring the fundamentals, such as synchronization and control. The aim of the book is to give to readers a comprehensive view of the main concepts of nonlinear dynamics to help them better understand complex systems and their control through the use of electronics devices.


"This textbook offers a very comprehensive, very clear and unique course on nonlinear dynamics, synchronization and chaos control by using electronic circuits. The exercises, the numerical examples with MATLAB and laboratory experiments make it an extremely useful tool for under-graduated students or beginners in this domain."

Françoise Lamnabhi-Lagarrigue, CNRS, France

Table of Contents


Chapter 1 Introduction to nonlinear systems

1.1 Classification of complex systems

1.2 First-order systems

1.3 Numerical solutions of differential equations

1.4 Exercises

Chapter 2 The logistic map and elements of complex system dynamics

2.1 The logistic map

2.2 Equilibrium points and periodic solutions of the logistic map

2.3 Chaos in the logistic map

2.4 Intermittency

2.5 Bifurcation diagram and Feigenbaum constant

2.6 Characterizing elements of chaotic behavior

2.6.1 Lyapunov exponents

2.7 Exercises

Chapter 3 Bifurcations

3.1 Introduction to bifurcations in dynamical systems

3.2 Elementary bifurcations

3.3 Bifurcations towards catastrophes

3.4 Exercises

Chapter 4 Oscillators

4.1 Hopf bifurcation

4.2 Examples of oscillations and oscillators

4.3 Genesis of electronic oscillators

4.4 Li´enard systems

4.5 Dynamics of the van der Pol oscillator

4.6 Lur’e systems and the design of oscillators

4.7 Describing functions: essential elements

4.8 Hewlett oscillator

4.9 2D maps

4.10 Summary

4.11 Exercises

Chapter 5 Strange attractors and continuous-time chaotic systems

5.1 Features of chaos in continuous-time systems

5.2 Genesis of chaotic oscillations: the Chua’s circuit

5.3 Canonical chaotic attractors and their bifurcation diagrams

5.4 Further essential aspects of chaotic systems

5.5 Chaotic dynamics in Lur’e systems

5.6 Hyperchaotic circuits

5.7 Summary

5.8 Exercises

Chapter 6 Cellular Nonlinear Networks

6.1 CNN: basic notations

6.2 CNNs: main aspects

6.3 Cloning templates and features of CNNs

6.4 The CNN as a generator of nonlinear dynamics

6.5 Reaction-diffusion CNN

6.6 Summary

6.7 Exercises

Chapter 7 Synchronization and chaos control

7.1 Introduction

7.2 Principles of synchronization of nonlinear dynamical systems

7.3 Schemes for unidirectional synchronization

7.4 Synchronization via diffusive coupling

7.5 Principles of chaos control

7.6 Strategies for chaos control

7.7 General remarks on chaos control

7.8 Exercises

Chapter 8 Experiments and applications

8.1 Hewlett oscillator

8.2 Van der Pol oscillator

8.3 An "elegant" oscillator

8.4 Synchronization of two Hewlett oscillators

8.5 Multilayer CNN cell with slow-fast dynamics for RD-CNN

8.6 Non-autonomous multilayer CNN with chaotic behavior

8.7 Multilayer SC-CNN with Chua’s circuit dynamics

8.8 Multilayer SC-CNN implementing hyperchaotic Chua’s circuit dynamics

8.9 A SC-CNN chaotic circuit with memristor

8.10 Synchronization of two Chua’s dynamics with diffusive coupling

8.11 Chaos encryption

8.12 Qualitative chaos-based sensors

8.13 Chaos control experiment

8.14 Logistic map with Arduino

8.15 Networks of SC-CNN Chua’s circuits

8.16 Exercises



About the Authors

Arturo Buscarino graduated in Computer Science Engineering in 2004 and received his Ph.D. in Electronics and Automation Engineering in 2008, at the University of Catania, Italy. Currently, he is a Technical Assistant at the University of Catania and teaches Modeling and Optimization at the Laura Magistrale in Management Engineering. He collaborates with the EUROFusion Consortium, ENEA Frascati, and JET Culham, UK. Dr. Buscarino has been a visiting researcher at the University of Wisconsin-Madison, US. His scientific interests include nonlinear circuits and systems, chaos and synchronization, complex networks, control systems, Cellular Nonlinear Networks, and plasma engineering. He is Associate Editor of Cogent Engineering. Dr. Buscarino has published one research monography on nonlinear circuits, and more than 60 papers on refereed international journals and international conference proceedings.

Luigi Fortuna received the degree of electrical engineering (cum laude) from the University of Catania, Italy, in 1977. He is a Full Professor of System Theory at the University of Catania. From 2005 to 2012, he was the Dean of the Engineering Faculty. He has been a visiting researcher at the Joint European Torus in Abingdon UK. He currently teaches complex adaptive systems and robust control. He has published 14 scientific books and 12 industrial patents. Dr. Fortuna has been a consultant of STMicroelectronics and other companies. He is the Editor in Chief of the SpringerBrief Series on Nonlinear Circuits. His scientific interests include robust control, Tokamak machine control, complex engineering, nonlinear circuits, chaos, cellular neural networks, robotics, and smart devices for control. Additionally, he is an IEEE Fellow.

Mattia Frasca graduated in Electronics Engineering in 2000 and received his Ph.D. in Electronics and Automation Engineering in 2003, at the University of Catania, Italy. Currently, he is a research associate at the University of Catania, where he also teaches process control. His scientific interests include nonlinear systems and chaos, complex networks, and bio-inspired robotics. He is Associate Editor of the International Journal of Bifurcations and Chaos, and Editor of Chaos, Solitons and Fractals. He is the general chair for the next edition of the European Conference on Circuits Theory and Design to be held in Catania. Additionally, he is co-author of one research monograph with Springer, three with World Scientific, and one book on Optimal and robust control with CRC Press. Dr. Frasca has published more than 250 papers on refereed international journals and international conference proceedings and is co-author of two international patents. He is an IEEE Senior and also a member of the Board of the Italian Society for Chaos and Complexity (SICC).

Subject Categories

BISAC Subject Codes/Headings:
TECHNOLOGY & ENGINEERING / Electronics / Circuits / General