Dynamics of Complex Interconnected Biological Systems

  • Thomas L. Vincent
  • Alistair I. Mees
  • Leslie S. Jennings

Part of the Mathematical Modelling book series (MMO, volume 6)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Modelling

    1. Front Matter
      Pages 1-1
    2. Michael A. B. Deakin
      Pages 2-16
    3. M. R. Myerscough, P. K. Maini, J. D. Murray, K. H. Winters
      Pages 65-83
  3. Tools

    1. Front Matter
      Pages 103-103
    2. Alistair I. Mees
      Pages 104-124
    3. Kevin Judd
      Pages 139-154
    4. Walter J. Grantham, Amit M. Athalye
      Pages 155-174
  4. Games

  5. Back Matter
    Pages 333-333

About this book


This volume contains the proceedings of the U.S. Australia workshop on Complex Interconnected Biological Systems held in Albany, Western Australia January 1-5, 1989. The workshop was jointly sponsored by the Department of Industry, Trade and Commerce (Australia), and the Na­ tional Science Foundation (USA) under the US-Australia agreement. Biological systems are typically hard to study mathematically. This is particularly so in the case of systems with strong interconnections, such as ecosystems or networks of neurons. In the past few years there have been substantial improvements in the mathematical tools available for study­ ing complexity. Theoretical advances include substantially improved un­ derstanding of the features of nonlinear systems that lead to important behaviour patterns such as chaos. Practical advances include improved modelling techniques, and deeper understanding of complexity indicators such as fractal dimension. Game theory is now playing an increasingly important role in under­ standing and describing evolutionary processes in interconnected systems. The strategies of individuals which affect each other's fitness may be incor­ porated into models as parameters. Strategies which have the property of evolutionary stabilty result from particular parameter values which may be the main feature of living determined using game theoretic methods. Since systems is that they evolve, it seems appropriate that any model used to describe such systems should have this feature as well. Evolutionary game theory should lead the way in the development of such methods.


Mathematica behavior dynamics ecosystem modeling

Editors and affiliations

  • Thomas L. Vincent
    • 1
  • Alistair I. Mees
    • 2
  • Leslie S. Jennings
    • 2
  1. 1.Department of Aerospace and Mechanical EngineeringUniversity of ArizonaTucsonUSA
  2. 2.Mathematics DepartmentUniversity of Western AustraliaNedlandsAustralia

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