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Dynamics of Complex Interconnected Biological Systems

  • Book
  • © 1990

Overview

Editors:
  1. Thomas L. Vincent

    1. Department of Aerospace and Mechanical Engineering, University of Arizona, Tucson, USA

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  2. Alistair I. Mees

    1. Mathematics Department, University of Western Australia, Nedlands, Australia

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    You can also search for this editor in PubMed   Google Scholar

  3. Leslie S. Jennings

    1. Mathematics Department, University of Western Australia, Nedlands, Australia

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    You can also search for this editor in PubMed   Google Scholar

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

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Table of contents (16 chapters)

  1. Front Matter

    Pages i-xii
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  2. Modelling

    1. Front Matter

      Pages 1-1
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    2. Modelling Biological Systems

      • Michael A. B. Deakin
      Pages 2-16

    3. A Length-Structured Model of the Western Rock Lobster Fishery of Western Australia

      • N. G. Hall, R. S. Brown, N. Caputi
      Pages 17-39

    4. Legumes at Loggerheads: Modelling Competition Between Two Strains of Sub-Clover

      • Anthony G. Pakes
      Pages 40-64

    5. Two Dimensional Pattern Formation In a Chemotactic System

      • M. R. Myerscough, P. K. Maini, J. D. Murray, K. H. Winters
      Pages 65-83

    6. Mathematical Modelling of the Control of Blood Glucose Levels in Diabetics by Insulin Infusion

      • Michael E. Fisher
      Pages 84-102

  3. Tools

    1. Front Matter

      Pages 103-103
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    2. Modelling Complex Systems

      • Alistair I. Mees
      Pages 104-124

    3. Detecting Folds in Chaotic Processes By Mapping the Convex Hull

      • J. N. Glover
      Pages 125-138

    4. Chaos in Complex Systems

      • Kevin Judd
      Pages 139-154

    5. A Chaotic System: Discretization and Control

      • Walter J. Grantham, Amit M. Athalye
      Pages 155-174

    6. Impulsive Evolution Equations and Population Models

      • Phil Diamond
      Pages 175-203

    7. Scaling as a Tool for the Analysis of Biological Models

      • D. L. S. McElwain
      Pages 204-217

    8. A Numerical Algorithm for Constrained Optimal Control Problems with Applications to Harvesting

      • L. S. Jennings, K. L. Teo
      Pages 218-234
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Keywords

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.

Editors and Affiliations

  • Department of Aerospace and Mechanical Engineering, University of Arizona, Tucson, USA

    Thomas L. Vincent

  • Mathematics Department, University of Western Australia, Nedlands, Australia

    Alistair I. Mees, Leslie S. Jennings

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