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Synchronization in Networks of Nonlinear Circuits

Essential Topics with MATLAB® Code

  • Book
  • © 2018

Overview

Authors:
  1. Mattia Frasca

    1. Department of Electrical, Electronic and Computer Engineering, University of Catania, Catania, Italy

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  2. Lucia Valentina Gambuzza

    1. Department of Electrical, Electronic and Computer Engineering, University of Catania, Catania, Italy

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  3. Arturo Buscarino

    1. Department of Electrical, Electronic and Computer Engineering, University of Catania, Catania, Italy

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  4. Luigi Fortuna

    1. Department of Electrical, Electronic and Computer Engineering, University of Catania, Catania, Italy

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  • Broadens readers’ understanding of novel research on chimera states
  • Clarifies the main aspects of synchronization theory
  • Includes codes for various techniques introduced in the text to encourage reader experimentation

Part of the book series: SpringerBriefs in Applied Sciences and Technology (BRIEFSAPPLSCIENCES)

Part of the book sub series: SpringerBriefs in Nonlinear Circuits (BRIEFSNONLINCIRC)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-viii
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  2. Introduction

    • Mattia Frasca, Lucia Valentina Gambuzza, Arturo Buscarino, Luigi Fortuna
    Pages 1-14

  3. Global Synchronization

    • Mattia Frasca, Lucia Valentina Gambuzza, Arturo Buscarino, Luigi Fortuna
    Pages 15-38

  4. Chimera States

    • Mattia Frasca, Lucia Valentina Gambuzza, Arturo Buscarino, Luigi Fortuna
    Pages 39-56

  5. Cluster Synchronization

    • Mattia Frasca, Lucia Valentina Gambuzza, Arturo Buscarino, Luigi Fortuna
    Pages 57-73

  6. Remote and Relay Synchronization

    • Mattia Frasca, Lucia Valentina Gambuzza, Arturo Buscarino, Luigi Fortuna
    Pages 75-91

  7. Synchronization in Time-Varying Networks

    • Mattia Frasca, Lucia Valentina Gambuzza, Arturo Buscarino, Luigi Fortuna
    Pages 93-107

  8. Conclusive Remarks

    • Mattia Frasca, Lucia Valentina Gambuzza, Arturo Buscarino, Luigi Fortuna
    Pages 109-109
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About this book

This book addresses synchronization in networks of coupled systems. It illustrates the main aspects of the phenomenon through concise theoretical results and code, allowing readers to reproduce them and encouraging readers to pursue their own experimentation.

The book begins by introducing the mathematical representation of nonlinear circuits and the code for their simulation. This is followed by a brief account of the concept of the complex network, which describes the main aspects of complex networks and the main model types, with a particular focus on the code used to study and reproduce the models. 

The focus then shifts to the process through which independent nonlinear circuits that follow different trajectories without coupling share some properties of their motion: synchronization. The authors present the main techniques for studying synchronization in complex networks, including the major measures, the stability properties and control techniques. The book then moves on to advanced topics in synchronization of complex networks by examining forms of synchronization in which not all the units share the same trajectory, namely chimera states, clustering synchronization, and relay and remote synchronization. Simple codes for experimentation with these topics and control methods are also provided. In closing, the book addresses the problem of synchronization in time-varying networks.

Reviews

“It is evident that the author worked hard to find, organize, and write up the wide variety of standard results that appear in the textbook. … the writing is user-friendly and the proofs include all the necessary details. The textbook is essentially a list of definitions, theorems, and proofs … . the book does gather together a wide range of topics and includes more computational details than many other such works.” (Russel Arthur Gordon, Mathematical Reviews, October, 2018)​

Authors and Affiliations

  • Department of Electrical, Electronic and Computer Engineering, University of Catania, Catania, Italy

    Mattia Frasca, Lucia Valentina Gambuzza, Arturo Buscarino, Luigi Fortuna

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