《生物数学(第2卷第3版)》是springer《生物数学丛书》之一，是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。本书由莫里著。

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

 7.1 Evolution and Morphogenesis

 7.2 Evolution and Morphogenetic Rules in Cartilage Formation in the Vertebrate Limb

 7.3 Teratologies (Monsters)

 7.4 Developmental Constraints, Morphogenetic Rules and the Consequences for Evolution

8. A Mechanical Theory of Vascular Network Formation

 8.1 Biological Background and Motivation

 8.2 Cell-Extracellular Matrix Interactions for Vasculogenesis

 8.3 Parameter Values

 8.4 Analysis of the Model Equations

 8.5 Network Patterns: Numerical Simulations and Conclusions

9. Epidermal Wound Healing

 9.1 Brief History of Wound Healing

 9.2 Biological Background: Epidermal Wounds

 9.3 Model for Epidermal Wound Healing

 9.4 Nondimensional Form, Linear Stability and Parameter Values

 9.5 Numerical Solution for the Epidermal Wound Repair Model

 9.6 Travelling Wave Solutions for the Epidermal Model

 9.7 Clinical Implications of the Epidermal Wound Model

 9.8 Mechanisms of Epidermal Repair in Embryos

 9.9 Actin Alignment in Embryonic Wounds: A Mechanical Model

 9.10 Mechanical Model with Stress Alignment of the Actin Filaments in Two Dimensions

10. Dermal Wound Healing

 10.1 Background and Motivation--General and Biological

 10.2 Logic of Wound Healing and Initial Models

 10.3 Brief Review of Subsequent Developments

 10.4 Model for Fibroblast-Driven Wound Healing: Residual Strain and Tissue Remodelling

 10.5 Solutions of the Model Equations and Comparison with Experiment

 10.6 Wound Healing Model of Cook (1995)

 10.7 Matrix Secretion and Degradation

 10.8 Cell Movement in an Oriented Environment

 10.9 Model System for Dermal Wound Healing with Tissue Structure

 10.10 One-Dimensional Model for the Structure of Pathological Scars

 10.11 Open Problems in Wound Healing

 10.12 Concluding Remarks on Wound Healing

11. Growth and Control of Brain Tumours

 11.1 Medical Background

 11.2 Basic Mathematical Model of Glioma Growth and Invasion

 11.3 Tumour Spread In Vitro: Parameter Estimation

 11.4 Tumour Invasion in the Rat Brain

 11.5 Tumour Invasion in the Human Brain

 11.6 Modelling Treatment Scenarios: General Comments

 11.7 Modelling Tumour Resection in Homogeneous Tissue

 11.8 Analytical Solution for Tumour Recurrence After Resection

 11.9 Modelling Surgical Resection with Brain Tissue Heterogeneity

 11.10 Modelling the Effect of Chemotherapy on Tumour Growth

 11.11 Modelling Tumour Polyclonality and Cell Mutation

12. Neural Models of Pattern Formation

 12.1 Spatial Patterning in Neural Firing with a Simple Activation-inhibition Model

 12.2 A Mechanism for Stripe Formation in the Visual Cortex

 12.3 A Model for the Brain Mechanism Underlying Visual Hallucination Patterns

 12.4 Neural Activity Model for Shell Patterns

 12.5 Shamanism and Rock Art

 Exercises

13. Geographic Spread and Control of Epidemics

 13.1 Simple Model for the Spatial Spread of an Epidemic

 13.2 Spread of the Black Death in Europe 1347-1350

 13.3 Brief History of Rabies: Facts and Myths

 13.4 The Spatial Spread of Rabies Among Foxes Ⅰ: Background and Simple Model

 13.5 The Spatial Spread of Rabies Among Foxes Ⅱ: Three-Species (SIR) Model

 13.6 Control Strategy Based on Wave Propagation into a Nonepidemic Region: Estimate of Width of a Rabies Barrier

 13.7 Analytic Approximation for the Width of the Rabies Control Break

 13.8 Two-Dimensional Epizootic Fronts and Effects of Variable Fox Densities:

 Quantitative Predictions for a Rabies Outbreak in England

 13.9 Effect of Fox Immunity on the Spatial Spread of Rabies

 Exercises

14. Wolf Territoriality, Wolf-Deer Interaction and Survival

 14.1 Introduction and Wolf Ecology

 14.2 Models for Wolf Pack Territory Formation: Single Pack--Home Range Model

 14.3 Multi-Wolf Pack Territorial Model

 14.4 Wolf-Deer Predator-Prey Model

 14.5 Concluding Remarks on Wolf Territoriality and Deer Survival

 14.6 Coyote Home Range Patterns

 14.7 Chippewa and Sioux Intertfibal Conflict c1750-1850

Appendix

A General Results for the Laplacian Operator in Bounded Domains

Bibliography

Index