生物数学

CONTENTS,VOLUME Ⅱ

Preface to the Third Edition

Preface to the First Edition

1.Multi-Species Waves and Practical Applications

1.1 Intuitive Expectations

1.2 Waves of Pursuit and Evasion in Predator-Prey Systems

1.3 Competition Model for the Spatial Spread of the Grey Squirrel in Britain

1.4 Spread of Genetically Engineered Organisms

1.5 Travelling Fronts in the Belousov-Zhabotinskii Reaction

1.6 Waves in Excitable Media

1.7 Travelling Wave Trains in Reaction Diffusion Systems with Oscillatory Kinetics

1.8 Spiral Waves

1.9 Spiral Wave Solutions of Reaction Diffusion Systems

Exercises

2.Spatial Pattern Formation with Reaction Diffusion Systems

2.1 Role of Pattern in Biology

2.2 Reaction Diffusion （Taring） Mechanisms

2.3 General Conditions for Diffusion-Driven Instability: Linear Stability Analysis and Evolution of Spatial Pattern

2.4 Detailed Analysis of Pattern Initiation in a Reaction Diffusion Mechanism

2.5 Dispersion Relation luring Space,Scale and Geometry Effects in Pattern Formation Models

2.6 Mode Selection and the Dispersion Relation

2.7 Pattern Generation with Single-Species Models: Spatial Heterogeneity with the Spruce Budworm Model

2.8 Spatial Patterns in Scalar Population Interaction Diffusion

Equations with Convection: Ecological Control Strategies

2.9 Nonexistence of Spatial Patterns in Reaction Diffusion Systems: General and Particular Results

Exercises

3.Animal Coat Patterns and Other Practical Applications of Reaction Diffusion Mechanisms

3.1 Mammalian Coat Patterns——How the Leopard Got Its Spots

3.2 Teratologies: Examples of Animal Coat Pattern Abnormalities

3.3 A Pattern Formation Mechanism for Butterfly Wing Patterns

3.4 Modelling Hair Patterns in a Whorl in Acetabularia

4.Pattern Formation on Growing Domains: Alligators and Snakes

4.1 Stripe Pattern Formation in the Alligator: Experiments

4.2 Modelling Concepts: Determining the Time of Stripe Formation

4.3 Stripes and Shadow Stripes on the Alligator

4.4 Spatial Patterning of Teeth Primordia in the Alligator: Background and Relevance

4.5 Biology of Tooth Initiation

4.6 Modelling Tooth Primordium Initiation: Background

4.7 Model Mechanism for Alligator Teeth Patterning

4.8 Results and Comparison with Experimental Data

4.9 Prediction Experiments

4.10 Concluding Remarks on Alligator Tooth Spatial Patterning

4.11 Pigmentation Pattern Formation on Snakes

4.12 Cell-Chemotaxis Model Mechanism

4.13 Simple and Complex Snake Pattern Elements

4.14 Propagating Pattern Generation with the Cell-Chemotaxis System

5.Bacterial Patterns and Chemotaxis

5.1 Background and Experimental Results

5.2 Model Mechanism for E coil in the Semi-Solid Experiments

5.3 Liquid Phase Model: Intuitive Analysis of Pattern Formation

5.4 Interpretation of the Analytical Results and Numerical Solutions

5.5 Semi-Solid Phase Model Mechanism for S typhimurium

5.6 Linear Analysis of the Basic Semi-Solid Model

5.7 Brief Outline and Results of the Nonlinear Analysis

5.8 Simulation Results,Parameter Spaces and Basic Patterns

5.9 Numerical Results with Initial Conditions from the~Experiments

5.10 Swarm Ring Patterns with the Semi-Solid Phase Model Mechanism

5.11 Branching Patterns in Bacillus subtilis

6.Mechanical Theory for Generating Pattern and Form in Development

6.1 Introduction,Motivation and Background Biology

6.2 Mechanical Model for Mesenchymal Morphogenesis

6.3 Linear Analysis,Dispersion Relation and Pattern Formation Potential

6.4 Simple Mechanical Models Which Generate Spatial Patterns with Complex Dispersion Relations

6.5 Periodic Patterns of Feather Germs

6.6 Cartilage Condensations in Limb Morphogenesis and Morphogenetic Rules

6.7 Embryonic Fingerprint Formation

6.8 Mechanochemical Model for the Epidermis

6.9 Formation of Microvilli

6.10 Complex Pattern Formation and Tissue Interaction Models

Exercises

7.Evolution,Morphogenetic Laws,Developmental Constraints and Teratologies

8.A Mechanical Theory of Vascular Network Formation

9.Epidermal Wound Healing

10.Dermal Wound Healing

11.Growth and Control of Brain Tumours

12.Neural Models of Pattern Formation

13.Geographic Spread and Control of Epidemics

14.Wolf Territoriality,Wolf-Deer Interaction and Survival

Appendix

A General Results for the Laplacian Operator in Bounded Domains

Bibliography

Index

《生物数学（第2卷·第3版）》近代生物数学方面的名著。第三版，在原来版本的基础上做了全面修订。近年来这个科目的茁壮成长和新知识点的不断涌现，新的版本将原来的一卷集分成上下两卷，扩大了知识容量，第二卷绝大多数是新增知识点。书中对生物学中的反应扩散方程和形态发生学的数学理论及最新研究成果作了全面介绍，是学习与研究生物数学的一部不可多得的参考书。