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| Preface to the Third Edition | |
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| Preface to the First Edition | |
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| Multi-Species Waves and Practical Applications | |
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| Intuitive Expectations | |
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| Waves of Pursuit and Evasion in Predator-Prey Systems | |
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| Competition Model for the Spatial Spread of the Grey Squirrel in Britain | |
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| Spread of Genetically Engineered Organisms | |
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| Travelling Fronts in the Belousov-Zhabotinskii Reaction | |
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| Waves in Excitable Media | |
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| Travelling Wave Trains in Reaction Diffusion Systems with Oscillatory Kinetics | |
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| Spiral Waves | |
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| Spiral Wave Solutions of [lambda]-[omega] Reaction Diffusion Systems | |
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| Exercises | |
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| Spatial Pattern Formation with Reaction Diffusion Systems | |
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| Role of Pattern in Biology | |
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| Reaction Diffusion (Turing) Mechanisms | |
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| General Conditions for Diffusion-Driven Instability: Linear Stability Analysis and Evolution of Spatial Pattern | |
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| Detailed Analysis of Pattern Initiation in a Reaction Diffusion Mechanism | |
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| Dispersion Relation, Turing Space, Scale and Geometry Effects in Pattern Formation Models | |
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| Mode Selection and the Dispersion Relation | |
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| Pattern Generation with Single-Species Models: Spatial Heterogeneity with the Spruce Budworm Model | |
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| Spatial Patterns in Scalar Population Interaction Diffusion Equations with Convection: Ecological Control Strategies | |
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| Nonexistence of Spatial Patterns in Reaction Diffusion Systems: General and Particular Results | |
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| Exercises | |
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| Animal Coat Patterns and Other Practical Applications of Reaction Diffusion Mechanisms | |
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| Mammalian Coat Patterns--'How the Leopard Got Its Spots' | |
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| Teratologies: Examples of Animal Coat Pattern Abnormalities | |
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| A Pattern Formation Mechanism for Butterfly Wing Patterns | |
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| Modelling Hair Patterns in a Whorl in Acetabularia | |
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| Pattern Formation on Growing Domains: Alligators and Snakes | |
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| Stripe Pattern Formation in the Alligator: Experiments | |
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| Modelling Concepts: Determining the Time of Stripe Formation | |
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| Stripes and Shadow Stripes on the Alligator | |
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| Spatial Patterning of Teeth Primordia in the Alligator: Background and Relevance | |
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| Biology of Tooth Initiation | |
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| Modelling Tooth Primordium Initiation: Background | |
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| Model Mechanism for Alligator Teeth Patterning | |
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| Results and Comparison with Experimental Data | |
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| Prediction Experiments | |
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| Concluding Remarks on Alligator Tooth Spatial Patterning | |
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| Pigmentation Pattern Formation on Snakes | |
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| Cell-Chemotaxis Model Mechanism | |
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| Simple and Complex Snake Pattern Elements | |
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| Propagating Pattern Generation with the Cell-Chemotaxis System | |
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| Bacterial Patterns and Chemotaxis | |
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| Background and Experimental Results | |
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| Model Mechanism for E. coli in the Semi-Solid Experiments | |
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| Liquid Phase Model: Intuitive Analysis of Pattern Formation | |
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| Interpretation of the Analytical Results and Numerical Solutions | |
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| Semi-Solid Phase Model Mechanism for S. typhimurium | |
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| Linear Analysis of the Basic Semi-Solid Model | |
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| Brief Outline and Results of the Nonlinear Analysis | |
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| Simulation Results, Parameter Spaces and Basic Patterns | |
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| Numerical Results with Initial Conditions from the Experiments | |
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| Swarm Ring Patterns with the Semi-Solid Phase Model Mechanism | |
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| Branching Patterns in Bacillus subtilis | |
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| Mechanical Theory for Generating Pattern and Form in Development | |
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| Introduction, Motivation and Background Biology | |
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| Mechanical Model for Mesenchymal Morphogenesis | |
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| Linear Analysis, Dispersion Relation and Pattern Formation Potential | |
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| Simple Mechanical Models Which Generate Spatial Patterns with Complex Dispersion Relations | |
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| Periodic Patterns of Feather Germs | |
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| Cartilage Condensations in Limb Morphogenesis and Morphogenetic Rules | |
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| Embryonic Fingerprint Formation | |
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| Mechanochemical Model for the Epidermis | |
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| Formation of Microvilli | |
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| Complex Pattern Formation and Tissue Interaction Models | |
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| Exercises | |
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| Evolution, Morphogenetic Laws, Developmental Constraints and Teratologies | |
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| Evolution and Morphogenesis | |
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| Evolution and Morphogenetic Rules in Cartilage Formation in the Vertebrate Limb | |
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| Teratologies (Monsters) | |
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| Developmental Constraints, Morphogenetic Rules and the Consequences for Evolution | |
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| A Mechanical Theory of Vascular Network Formation | |
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| Biological Background and Motivation | |
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| Cell-Extracellular Matrix Interactions for Vasculogenesis | |
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| Parameter Values | |
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| Analysis of the Model Equations | |
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| Network Patterns: Numerical Simulations and Conclusions | |
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| Epidermal Wound Healing | |
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| Brief History of Wound Healing | |
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| Biological Background: Epidermal Wounds | |
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| Model for Epidermal Wound Healing | |
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| Nondimensional Form, Linear Stability and Parameter Values | |
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| Numerical Solution for the Epidermal Wound Repair Model | |
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| Travelling Wave Solutions for the Epidermal Model | |
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| Clinical Implications of the Epidermal Wound Model | |
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| Mechanisms of Epidermal Repair in Embryos | |
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| Actin Alignment in Embryonic Wounds: A Mechanical Model | |
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| Mechanical Model with Stress Alignment of the Actin Filaments in Two Dimensions | |
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| Dermal Wound Healing | |
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| Background and Motivation--General and Biological | |
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| Logic of Wound Healing and Initial Models | |
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| Brief Review of Subsequent Developments | |
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| Model for Fibroblast-Driven Wound Healing: Residual Strain and Tissue Remodelling | |
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| Solutions of the Model Equations and Comparison with Experiment | |
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| Wound Healing Model of Cook (1995) | |
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| Matrix Secretion and Degradation | |
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| Cell Movement in an Oriented Environment | |
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| Model System for Dermal Wound Healing with Tissue Structure | |
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| One-Dimensional Model for the Structure of Pathological Scars | |
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| Open Problems in Wound Healing | |
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| Concluding Remarks on Wound Healing | |
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| Growth and Control of Brain Tumours | |
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| Medical Background | |
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| Basic Mathematical Model of Glioma Growth and Invasion | |
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| Tumour Spread In Vitro: Parameter Estimation | |
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| Tumour Invasion in the Rat Brain | |
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| Tumour Invasion in the Human Brain | |
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| Modelling Treatment Scenarios: General Comments | |
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| Modelling Tumour Resection in Homogeneous Tissue | |
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| Analytical Solution for Tumour Recurrence After Resection | |
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| Modelling Surgical Resection with Brain Tissue Heterogeneity | |
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| Modelling the Effect of Chemotherapy on Tumour Growth | |
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| Modelling Tumour Polyclonality and Cell Mutation | |
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| Neural Models of Pattern Formation | |
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| Spatial Patterning in Neural Firing with a Simple Activation-Inhibition Model | |
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| A Mechanism for Stripe Formation in the Visual Cortex | |
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| A Model for the Brain Mechanism Underlying Visual Hallucination Patterns | |
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| Neural Activity Model for Shell Patterns | |
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| Shamanism and Rock Art | |
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| Exercises | |
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| Geographic Spread and Control of Epidemics | |
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| Simple Model for the Spatial Spread of an Epidemic | |
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| Spread of the Black Death in Europe 1347-1350 | |
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| Brief History of Rabies: Facts and Myths | |
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| The Spatial Spread of Rabies Among Foxes I: Background and Simple Model | |
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| The Spatial Spread of Rabies Among Foxes II: Three-Species (SIR) Model | |
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| Control Strategy Based on Wave Propagation into a Nonepidemic Region: Estimate of Width of a Rabies Barrier | |
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| Analytic Approximation for the Width of the Rabies Control Break | |
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| Two-Dimensional Epizootic Fronts and Effects of Variable Fox Densities: Quantitative Predictions for a Rabies Outbreak in England | |
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| Effect of Fox Immunity on the Spatial Spread of Rabies | |
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| Exercises | |
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| Wolf Territoriality, Wolf-Deer Interaction and Survival | |
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| Introduction and Wolf Ecology | |
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| Models for Wolf Pack Territory Formation: Single Pack--Home Range Model | |
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| Multi-Wolf Pack Territorial Model | |
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| Wolf-Deer Predator-Prey Model | |
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| Concluding Remarks on Wolf Territoriality and Deer Survival | |
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| Coyote Home Range Patterns | |
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| Chippewa and Sioux Intertribal Conflict c1750-1850 | |
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| Appendix | |
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| General Results for the Laplacian Operator in Bounded Domains | |
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| Bibliography | |
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| Index | |