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Symmetry in Complex Network Systems

Connecting Equivariant Bifurcation Theory with Engineering Applications

  • Visarath In
  • Antonio Palacios

Part of the Understanding Complex Systems book series (UCS)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Visarath In, Antonio Palacios
    Pages 1-35
  3. Visarath In, Antonio Palacios
    Pages 37-104
  4. Visarath In, Antonio Palacios
    Pages 105-125
  5. Visarath In, Antonio Palacios
    Pages 127-163
  6. Visarath In, Antonio Palacios
    Pages 165-227
  7. Visarath In, Antonio Palacios
    Pages 229-236
  8. Visarath In, Antonio Palacios
    Pages 237-293
  9. Visarath In, Antonio Palacios
    Pages 295-316
  10. Visarath In, Antonio Palacios
    Pages 317-337
  11. Visarath In, Antonio Palacios
    Pages 339-382
  12. Back Matter
    Pages 383-406

About this book

Introduction

This book bridges the current gap between the theory of symmetry-based dynamics and its application to model and analyze complex systems. As an alternative approach, the authors use the symmetry of the system directly to formulate the appropriate models, and also to analyze the dynamics. Complex systems with symmetry arise in a wide variety of fields, including communication networks, molecular dynamics, manufacturing businesses, ecosystems, underwater vehicle dynamics, celestial and spacecraft dynamics and continuum mechanics. A general approach for their analysis has been to derive a detailed model of their individual parts, connect the parts and note that the system contains some sort of symmetry, then attempt to exploit this symmetry in order to simplify numerical computations. This approach can result in highly complicated models that are difficult to analyze even numerically. The alternative approach, while nonstandard, is not entirely new among the mathematics community. However, there is much less familiarity with the techniques of symmetry-breaking bifurcation, as they apply to the engineering, design and fabrication, of complex systems, in particular, nonlinear sensor devices with special emphasis on the conceptualization and development of new technologies of magnetic sensors such as fluxgate magnetometers and SQUID (Superconducting Quantum Interference Devices), E-- (electric-field) sensors, and communication and navigation systems that require multiple frequencies of operation, such as radar and antenna devices as well as gyroscopic systems.

Keywords

Bistability Complex Systems Coupled Nonlinear Oscillators Nonlinear Dynamic Sensors Symmetry-breaking Bifurcation

Authors and affiliations

  • Visarath In
    • 1
  • Antonio Palacios
    • 2
  1. 1.Space and Naval Warfare Systems CenterSan DiegoUSA
  2. 2.Department of Mathematics, Nonlinear Dynamical Systems GroupSan Diego State UniversitySan DiegoUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-55545-3
  • Copyright Information Springer-Verlag GmbH Germany 2018
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Engineering
  • Print ISBN 978-3-662-55543-9
  • Online ISBN 978-3-662-55545-3
  • Series Print ISSN 1860-0832
  • Series Online ISSN 1860-0840
  • Buy this book on publisher's site