Boundaries of a Complex World

  • Andrei Ludu

Part of the Springer Series in Synergetics book series (SSSYN)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Arts and Nonlinear Systems: ‘Nonlineart’

    1. Front Matter
      Pages 1-2
    2. Andrei Ludu
      Pages 3-7
    3. Andrei Ludu
      Pages 79-105
  3. Mathematical Language

    1. Front Matter
      Pages 107-110
    2. Andrei Ludu
      Pages 111-154
    3. Andrei Ludu
      Pages 155-198
  4. Applications

    1. Front Matter
      Pages 199-201
    2. Andrei Ludu
      Pages 203-209
    3. Andrei Ludu
      Pages 211-227
    4. Andrei Ludu
      Pages 229-243
    5. Andrei Ludu
      Pages 245-337
    6. Andrei Ludu
      Pages 339-343
  5. Back Matter
    Pages 345-361

About this book

Introduction

The central theme of this book is the extent to which the structure of the free dynamical boundaries of a system controls the evolution of the system as a whole. Applying three orthogonal types of thinking - mathematical, constructivist and morphological, it illustrates these concepts using applications to selected problems from the social and life sciences, as well as economics.

 In a broader context, it introduces and reviews some modern mathematical approaches to the science of complex systems. Standard modeling approaches (based on non-linear differential equations, dynamic systems, graph theory, cellular automata, stochastic processes, or information theory) are suitable for studying local problems. However they cannot simultaneously take into account all the different facets and phenomena of a complex system, and new approaches are required to solve the challenging problem of correlations between phenomena at different levels and hierarchies, their self-organization and memory-evolutive aspects, the growth of additional structures and are ultimately required to explain why and how such complex systems can display both robustness and flexibility.

  This graduate-level text also addresses a broader interdisciplinary audience, keeping the mathematical level essentially uniform throughout the book, and involving only basic elements from calculus, algebra, geometry and systems theory.

 

Keywords

Dynamical Free Boundaries Mathematical Modeling of Complex Systems Robustness and Resilience of Complex Systems Boundaries in complex systems Art and complexity Boundaries and frames in science

Authors and affiliations

  • Andrei Ludu
    • 1
  1. 1.Department of MathematicsEmbry-Riddle Aeronautical UniversityDaytona BeachUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-49078-5
  • Copyright Information Springer-Verlag Berlin Heidelberg 2016
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-662-49076-1
  • Online ISBN 978-3-662-49078-5
  • Series Print ISSN 0172-7389
  • Series Online ISSN 2198-333X
  • About this book
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