Mathematical Aspects of Pattern Formation in Biological Systems

  • Juncheng Wei
  • Matthias Winter
Part of the Applied Mathematical Sciences book series (AMS, volume 189)

Table of contents

  1. Front Matter
    Pages I-XII
  2. Juncheng Wei, Matthias Winter
    Pages 1-12
  3. Juncheng Wei, Matthias Winter
    Pages 41-70
  4. Juncheng Wei, Matthias Winter
    Pages 91-106
  5. Juncheng Wei, Matthias Winter
    Pages 149-173
  6. Juncheng Wei, Matthias Winter
    Pages 175-247
  7. Juncheng Wei, Matthias Winter
    Pages 249-261
  8. Juncheng Wei, Matthias Winter
    Pages 263-270
  9. Juncheng Wei, Matthias Winter
    Pages 271-286
  10. Juncheng Wei, Matthias Winter
    Pages 287-295
  11. Juncheng Wei, Matthias Winter
    Pages 297-304
  12. Back Matter
    Pages 305-319

About this book

Introduction

This monograph is concerned with the mathematical analysis of patterns which are encountered in biological systems. It summarises, expands and relates results obtained in the field during the last fifteen years. It also links the results to biological applications and highlights their relevance to phenomena in nature. Of particular concern are large-amplitude patterns far from equilibrium in biologically relevant models.

The approach adopted in the monograph is based on the following paradigms:

• Examine the existence of spiky steady states in reaction-diffusion systems and select as observable patterns only the stable ones

• Begin by exploring spatially homogeneous two-component activator-inhibitor systems in one or two space dimensions

• Extend the studies by considering extra effects or related systems, each motivated by their specific roles in developmental biology, such as spatial inhomogeneities, large reaction rates, altered boundary conditions, saturation terms, convection, many-component systems.

Mathematical Aspects of Pattern Formation in Biological Systems will be of interest to graduate students and researchers who are active in reaction-diffusion systems, pattern formation and mathematical biology.

Keywords

Biological Systems Computational Biology Genetics Dynamics Localised Structures Mathematical Analysis Mathematical Biology Partial Differential Equations Pattern Formation Population Dynamics Reaction-Diffusion Systems Singular Perturbation Stability

Authors and affiliations

  • Juncheng Wei
    • 1
  • Matthias Winter
    • 2
  1. 1.Department of MathematicsThe Chinese University of Hong KongHong KongHong Kong SAR
  2. 2.Department of Mathematical SciencesBrunel UniversityUxbridgeUnited Kingdom

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4471-5526-3
  • Copyright Information Springer-Verlag London 2014
  • Publisher Name Springer, London
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4471-5525-6
  • Online ISBN 978-1-4471-5526-3
  • Series Print ISSN 0066-5452
  • Series Online ISSN 2196-968X
  • About this book