Applied Mathematical Sciences

Mathematical Aspects of Pattern Formation in Biological Systems

Authors: Wei, Juncheng, Winter, Matthias

  • Self-contained and includes rigorous proofs, often supported by numerical simulations
  • Contains an introduction to mathematical methods in nonlinear functional analysis and partial differential equations; Liapunov-Schmidt reduction and nonlocal eigenvalue problems
  • Includes links to biological applications; hydra development and regeneration, patterns on animal skins, embryo development, insect leg segmentation, left-right asymmetry of organisms, self-organisation of matter and consumer chains
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  • ISBN 978-1-4471-5526-3
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Hardcover $109.00
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  • ISBN 978-1-4471-5525-6
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  • Due: October 14, 2016
  • ISBN 978-1-4471-7261-1
  • Free shipping for individuals worldwide
Rent the ebook  
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About this book

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.

Reviews

From the book reviews:

“This book deals with the mathematical analysis of patterns encountered in biological systems, using a variety of functional analysis methods to prove the existence of solutions. … It is indeed written for advanced graduates and experts interested in the mathematics of pattern formation and reaction-diffusion equations. … this is a good reference source for various advanced theories and mathematical applications in this field.” (J. Michel Tchuenche, zbMATH, Vol. 1295, 2014)

Table of contents (13 chapters)

  • Introduction

    Wei, Juncheng (et al.)

    Pages 1-12

  • Existence of Spikes for the Gierer-Meinhardt System in One Dimension

    Wei, Juncheng (et al.)

    Pages 13-39

  • The Nonlocal Eigenvalue Problem (NLEP)

    Wei, Juncheng (et al.)

    Pages 41-70

  • Stability of Spikes for the Gierer-Meinhardt System in One Dimension

    Wei, Juncheng (et al.)

    Pages 71-89

  • Existence of Spikes for the Shadow Gierer-Meinhardt System

    Wei, Juncheng (et al.)

    Pages 91-106

Buy this book

eBook $79.99
price for USA (gross)
  • ISBN 978-1-4471-5526-3
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.00
price for USA
  • ISBN 978-1-4471-5525-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $109.00
price for USA
  • Customers within the U.S. and Canada please contact Customer Service at 1-800-777-4643, Latin America please contact us at +1-212-460-1500 (Weekdays 8:30am – 5:30pm ET) to place your order.
  • Due: October 14, 2016
  • ISBN 978-1-4471-7261-1
  • Free shipping for individuals worldwide
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Mathematical Aspects of Pattern Formation in Biological Systems
Authors
Series Title
Applied Mathematical Sciences
Series Volume
189
Copyright
2014
Publisher
Springer-Verlag London
Copyright Holder
Springer-Verlag London
Distribution Rights
Distribution rights for India: Delhi Book Store, New Delhi, India
eBook ISBN
978-1-4471-5526-3
DOI
10.1007/978-1-4471-5526-3
Hardcover ISBN
978-1-4471-5525-6
Softcover ISBN
978-1-4471-7261-1
Series ISSN
0066-5452
Edition Number
1
Number of Pages
XII, 319
Number of Illustrations and Tables
20 b/w illustrations
Topics