| Preface to the Third Edition | p. vii |
| Preface to the First Edition | p. xi |
| Multi-Species Waves and Practical Applications | p. 1 |
| Intuitive Expectations | p. 1 |
| Waves of Pursuit and Evasion in Predator-Prey Systems | p. 5 |
| Competition Model for the Spatial Spread of the Grey Squirrel in Britain | p. 12 |
| Spread of Genetically Engineered Organisms | p. 18 |
| Travelling Fronts in the Belousov-Zhabotinskii Reaction | p. 35 |
| Waves in Excitable Media | p. 41 |
| Travelling Wave Trains in Reaction Diffusion Systems with Oscillatory Kinetics | p. 49 |
| Spiral Waves | p. 54 |
| Spiral Wave Solutions of [lambda]-[omega] Reaction Diffusion Systems | p. 61 |
| Exercises | p. 67 |
| Spatial Pattern Formation with Reaction Diffusion Systems | p. 71 |
| Role of Pattern in Biology | p. 71 |
| Reaction Diffusion (Turing) Mechanisms | p. 75 |
| General Conditions for Diffusion-Driven Instability: Linear Stability Analysis and Evolution of Spatial Pattern | p. 82 |
| Detailed Analysis of Pattern Initiation in a Reaction Diffusion Mechanism | p. 90 |
| Dispersion Relation, Turing Space, Scale and Geometry Effects in Pattern Formation Models | p. 103 |
| Mode Selection and the Dispersion Relation | p. 113 |
| Pattern Generation with Single-Species Models: Spatial Heterogeneity with the Spruce Budworm Model | p. 120 |
| Spatial Patterns in Scalar Population Interaction Diffusion Equations with Convection: Ecological Control Strategies | p. 125 |
| Nonexistence of Spatial Patterns in Reaction Diffusion Systems: General and Particular Results | p. 130 |
| Exercises | p. 135 |
| Animal Coat Patterns and Other Practical Applications of Reaction Diffusion Mechanisms | p. 141 |
| Mammalian Coat Patterns--'How the Leopard Got Its Spots' | p. 142 |
| Teratologies: Examples of Animal Coat Pattern Abnormalities | p. 156 |
| A Pattern Formation Mechanism for Butterfly Wing Patterns | p. 161 |
| Modelling Hair Patterns in a Whorl in Acetabularia | p. 180 |
| Pattern Formation on Growing Domains: Alligators and Snakes | p. 192 |
| Stripe Pattern Formation in the Alligator: Experiments | p. 193 |
| Modelling Concepts: Determining the Time of Stripe Formation | p. 196 |
| Stripes and Shadow Stripes on the Alligator | p. 200 |
| Spatial Patterning of Teeth Primordia in the Alligator: Background and Relevance | p. 205 |
| Biology of Tooth Initiation | p. 207 |
| Modelling Tooth Primordium Initiation: Background | p. 213 |
| Model Mechanism for Alligator Teeth Patterning | p. 215 |
| Results and Comparison with Experimental Data | p. 224 |
| Prediction Experiments | p. 228 |
| Concluding Remarks on Alligator Tooth Spatial Patterning | p. 232 |
| Pigmentation Pattern Formation on Snakes | p. 234 |
| Cell-Chemotaxis Model Mechanism | p. 238 |
| Simple and Complex Snake Pattern Elements | p. 241 |
| Propagating Pattern Generation with the Cell-Chemotaxis System | p. 248 |
| Bacterial Patterns and Chemotaxis | p. 253 |
| Background and Experimental Results | p. 253 |
| Model Mechanism for E. coli in the Semi-Solid Experiments | p. 260 |
| Liquid Phase Model: Intuitive Analysis of Pattern Formation | p. 267 |
| Interpretation of the Analytical Results and Numerical Solutions | p. 274 |
| Semi-Solid Phase Model Mechanism for S. typhimurium | p. 279 |
| Linear Analysis of the Basic Semi-Solid Model | p. 281 |
| Brief Outline and Results of the Nonlinear Analysis | p. 287 |
| Simulation Results, Parameter Spaces and Basic Patterns | p. 292 |
| Numerical Results with Initial Conditions from the Experiments | p. 297 |
| Swarm Ring Patterns with the Semi-Solid Phase Model Mechanism | p. 299 |
| Branching Patterns in Bacillus subtilis | p. 306 |
| Mechanical Theory for Generating Pattern and Form in Development | p. 311 |
| Introduction, Motivation and Background Biology | p. 311 |
| Mechanical Model for Mesenchymal Morphogenesis | p. 319 |
| Linear Analysis, Dispersion Relation and Pattern Formation Potential | p. 330 |
| Simple Mechanical Models Which Generate Spatial Patterns with Complex Dispersion Relations | p. 334 |
| Periodic Patterns of Feather Germs | p. 345 |
| Cartilage Condensations in Limb Morphogenesis and Morphogenetic Rules | p. 350 |
| Embryonic Fingerprint Formation | p. 358 |
| Mechanochemical Model for the Epidermis | p. 367 |
| Formation of Microvilli | p. 374 |
| Complex Pattern Formation and Tissue Interaction Models | p. 381 |
| Exercises | p. 394 |
| Evolution, Morphogenetic Laws, Developmental Constraints and Teratologies | p. 396 |
| Evolution and Morphogenesis | p. 396 |
| Evolution and Morphogenetic Rules in Cartilage Formation in the Vertebrate Limb | p. 402 |
| Teratologies (Monsters) | p. 407 |
| Developmental Constraints, Morphogenetic Rules and the Consequences for Evolution | p. 411 |
| A Mechanical Theory of Vascular Network Formation | p. 416 |
| Biological Background and Motivation | p. 416 |
| Cell-Extracellular Matrix Interactions for Vasculogenesis | p. 417 |
| Parameter Values | p. 425 |
| Analysis of the Model Equations | p. 427 |
| Network Patterns: Numerical Simulations and Conclusions | p. 433 |
| Epidermal Wound Healing | p. 441 |
| Brief History of Wound Healing | p. 441 |
| Biological Background: Epidermal Wounds | p. 444 |
| Model for Epidermal Wound Healing | p. 447 |
| Nondimensional Form, Linear Stability and Parameter Values | p. 450 |
| Numerical Solution for the Epidermal Wound Repair Model | p. 451 |
| Travelling Wave Solutions for the Epidermal Model | p. 454 |
| Clinical Implications of the Epidermal Wound Model | p. 461 |
| Mechanisms of Epidermal Repair in Embryos | p. 468 |
| Actin Alignment in Embryonic Wounds: A Mechanical Model | p. 471 |
| Mechanical Model with Stress Alignment of the Actin Filaments in Two Dimensions | p. 482 |
| Dermal Wound Healing | p. 491 |
| Background and Motivation--General and Biological | p. 491 |
| Logic of Wound Healing and Initial Models | p. 495 |
| Brief Review of Subsequent Developments | p. 500 |
| Model for Fibroblast-Driven Wound Healing: Residual Strain and Tissue Remodelling | p. 503 |
| Solutions of the Model Equations and Comparison with Experiment | p. 507 |
| Wound Healing Model of Cook (1995) | p. 511 |
| Matrix Secretion and Degradation | p. 515 |
| Cell Movement in an Oriented Environment | p. 518 |
| Model System for Dermal Wound Healing with Tissue Structure | p. 521 |
| One-Dimensional Model for the Structure of Pathological Scars | p. 526 |
| Open Problems in Wound Healing | p. 530 |
| Concluding Remarks on Wound Healing | p. 533 |
| Growth and Control of Brain Tumours | p. 536 |
| Medical Background | p. 538 |
| Basic Mathematical Model of Glioma Growth and Invasion | p. 542 |
| Tumour Spread In Vitro: Parameter Estimation | p. 550 |
| Tumour Invasion in the Rat Brain | p. 559 |
| Tumour Invasion in the Human Brain | p. 563 |
| Modelling Treatment Scenarios: General Comments | p. 579 |
| Modelling Tumour Resection in Homogeneous Tissue | p. 580 |
| Analytical Solution for Tumour Recurrence After Resection | p. 584 |
| Modelling Surgical Resection with Brain Tissue Heterogeneity | p. 588 |
| Modelling the Effect of Chemotherapy on Tumour Growth | p. 594 |
| Modelling Tumour Polyclonality and Cell Mutation | p. 605 |
| Neural Models of Pattern Formation | p. 614 |
| Spatial Patterning in Neural Firing with a Simple Activation-Inhibition Model | p. 614 |
| A Mechanism for Stripe Formation in the Visual Cortex | p. 622 |
| A Model for the Brain Mechanism Underlying Visual Hallucination Patterns | p. 627 |
| Neural Activity Model for Shell Patterns | p. 638 |
| Shamanism and Rock Art | p. 655 |
| Exercises | p. 659 |
| Geographic Spread and Control of Epidemics | p. 661 |
| Simple Model for the Spatial Spread of an Epidemic | p. 661 |
| Spread of the Black Death in Europe 1347-1350 | p. 664 |
| Brief History of Rabies: Facts and Myths | p. 669 |
| The Spatial Spread of Rabies Among Foxes I: Background and Simple Model | p. 673 |
| The Spatial Spread of Rabies Among Foxes II: Three-Species (SIR) Model | p. 681 |
| Control Strategy Based on Wave Propagation into a Nonepidemic Region: Estimate of Width of a Rabies Barrier | p. 696 |
| Analytic Approximation for the Width of the Rabies Control Break | p. 700 |
| Two-Dimensional Epizootic Fronts and Effects of Variable Fox Densities: Quantitative Predictions for a Rabies Outbreak in England | p. 704 |
| Effect of Fox Immunity on the Spatial Spread of Rabies | p. 710 |
| Exercises | p. 720 |
| Wolf Territoriality, Wolf-Deer Interaction and Survival | p. 722 |
| Introduction and Wolf Ecology | p. 722 |
| Models for Wolf Pack Territory Formation: Single Pack--Home Range Model | p. 729 |
| Multi-Wolf Pack Territorial Model | p. 734 |
| Wolf-Deer Predator-Prey Model | p. 745 |
| Concluding Remarks on Wolf Territoriality and Deer Survival | p. 751 |
| Coyote Home Range Patterns | p. 753 |
| Chippewa and Sioux Intertribal Conflict c1750-1850 | p. 754 |
| Appendix | |
| General Results for the Laplacian Operator in Bounded Domains | p. 757 |
| Bibliography | p. 761 |
| Index | p. 791 |
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