Complexity Science: The Warwick Master's Course

[BOOK DESCRIPTION]

Complexity science is the study of systems with many interdependent components. Such systems - and the self-organization and emergent phenomena they manifest - lie at the heart of many challenges of global importance. This book is a coherent introduction to the mathematical methods used to understand complexity, with plenty of examples and real-world applications. It starts with the crucial concepts of self-organization and emergence, then tackles complexity in dynamical systems using differential equations and chaos theory. Several classes of models of interacting particle systems are studied with techniques from stochastic analysis, followed by a treatment of the statistical mechanics of complex systems. Further topics include numerical analysis of PDEs, and applications of stochastic methods in economics and finance. The book concludes with introductions to space-time phases and selfish routing. The exposition is suitable for researchers, practitioners and students in complexity science and related fields at advanced undergraduate level and above.

Preface                                            vii
        List of contributors                       xi
    1 Self-organisation and emergence              1  (47)
          Mario Nicodemi
          Yu-Xi Chau
          Christopher Oates
          Anas Rana
          Leigh Robinson
    2 Complexity and chaos in dynamical systems    48 (77)
          Yulia Timofeeva
    3 Interacting stochastic particle systems      125(85)
          Stefan Grosskinsky
    4 Statistical mechanics of complex systems     210(36)
          Ellak Somfai
    5 Numerical simulation of continuous systems   246(70)
          Colm Connaughton
    6 Stochastic methods in economics and          316(71)
    finance
          Vassili N. Kolokoltsov
    7 Space-time phases                            387(40)
          Robert S. MacKay
    8 Selfish routing                              427(14)
          Robert S. MacKay
Index                                              441