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
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