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| Preface to the Third Edition | |
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| Preface to the First Edition | |
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| Continuous Population Models for Single Species | |
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| Continuous Growth Models | |
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| Insect Outbreak Model: Spruce Budworm | |
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| Delay Models | |
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| Linear Analysis of Delay Population Models: Periodic Solutions | |
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| Delay Models in Physiology: Periodic Dynamic Diseases | |
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| Harvesting a Single Natural Population | |
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| Population Model with Age Distribution | |
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| Exercises | |
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| Discrete Population Models for a Single Species | |
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| Introduction: Simple Models | |
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| Cobwebbing: A Graphical Procedure of Solution | |
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| Discrete Logistic-Type Model: Chaos | |
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| Stability, Periodic Solutions and Bifurcations | |
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| Discrete Delay Models | |
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| Fishery Management Model | |
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| Ecological Implications and Caveats | |
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| Tumour Cell Growth | |
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| Exercises | |
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| Models for Interacting Populations | |
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| Predator-Prey Models: Lotka-Volterra Systems | |
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| Complexity and Stability | |
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| Realistic Predator-Prey Models | |
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| Analysis of a Predator-Prey Model with Limit Cycle Periodic Behaviour: Parameter Domains of Stability | |
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| Competition Models: Competitive Exclusion Principle | |
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| Mutualism or Symbiosis | |
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| General Models and Cautionary Remarks | |
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| Threshold Phenomena | |
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| Discrete Growth Models for Interacting Populations | |
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| Predator-Prey Models: Detailed Analysis | |
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| Exercises | |
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| Temperature-Dependent Sex Determination (TSD) | |
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| Biological Introduction and Historical Asides on the Crocodilia | |
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| Nesting Assumptions and Simple Population Model | |
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| Age-Structured Population Model for Crocodilia | |
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| Density-Dependent Age-Structured Model Equations | |
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| Stability of the Female Population in Wet Marsh Region I | |
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| Sex Ratio and Survivorship | |
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| Temperature-Dependent Sex Determination (TSD) Versus Genetic Sex Determination (GSD) | |
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| Related Aspects on Sex Determination | |
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| Exercise | |
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| Modelling the Dynamics of Marital Interaction: Divorce Prediction and Marriage Repair | |
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| Psychological Background and Data: Gottman and Levenson Methodology | |
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| Marital Typology and Modelling Motivation | |
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| Modelling Strategy and the Model Equations | |
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| Steady States and Stability | |
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| Practical Results from the Model | |
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| Benefits, Implications and Marriage Repair Scenarios | |
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| Reaction Kinetics | |
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| Enzyme Kinetics: Basic Enzyme Reaction | |
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| Transient Time Estimates and Nondimensionalisation | |
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| Michaelis-Menten Quasi-Steady State Analysis | |
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| Suicide Substrate Kinetics | |
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| Cooperative Phenomena | |
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| Autocatalysis, Activation and Inhibition | |
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| Multiple Steady States, Mushrooms and Isolas | |
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| Exercises | |
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| Biological Oscillators and Switches | |
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| Motivation, Brief History and Background | |
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| Feedback Control Mechanisms | |
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| Oscillators and Switches with Two or More Species: General Qualitative Results | |
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| Simple Two-Species Oscillators: Parameter Domain Determination for Oscillations | |
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| Hodgkin-Huxley Theory of Nerve Membranes: FitzHugh-Nagumo Model | |
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| Modelling the Control of Testosterone Secretion and Chemical Castration | |
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| Exercises | |
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| BZ Oscillating Reactions | |
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| Belousov Reaction and the Field-Koros-Noyes (FKN) Model | |
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| Linear Stability Analysis of the FKN Model and Existence of Limit Cycle Solutions | |
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| Nonlocal Stability of the FKN Model | |
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| Relaxation Oscillators: Approximation for the Belousov-Zhabotinskii Reaction | |
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| Analysis of a Relaxation Model for Limit Cycle Oscillations in the Belousov-Zhabotinskii Reaction | |
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| Exercises | |
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| Perturbed and Coupled Oscillators and Black Holes | |
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| Phase Resetting in Oscillators | |
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| Phase Resetting Curves | |
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| Black Holes | |
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| Black Holes in Real Biological Oscillators | |
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| Coupled Oscillators: Motivation and Model System | |
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| Phase Locking of Oscillations: Synchronisation in Fireflies | |
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| Singular Perturbation Analysis: Preliminary Transformation | |
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| Singular Perturbation Analysis: Transformed System | |
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| Singular Perturbation Analysis: Two-Time Expansion | |
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| Analysis of the Phase Shift Equation and Application to Coupled Belousov-Zhabotinskii Reactions | |
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| Exercises | |
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| Dynamics of Infectious Diseases | |
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| Historical Aside on Epidemics | |
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| Simple Epidemic Models and Practical Applications | |
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| Modelling Venereal Diseases | |
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| Multi-Group Model for Gonorrhea and Its Control | |
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| AIDS: Modelling the Transmission Dynamics of the Human Immunodeficiency Virus (HIV) | |
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| HIV: Modelling Combination Drug Therapy | |
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| Delay Model for HIV Infection with Drug Therapy | |
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| Modelling the Population Dynamics of Acquired Immunity to Parasite Infection | |
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| Age-Dependent Epidemic Model and Threshold Criterion | |
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| Simple Drug Use Epidemic Model and Threshold Analysis | |
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| Bovine Tuberculosis Infection in Badgers and Cattle | |
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| Modelling Control Strategies for Bovine Tuberculosis in Badgers and Cattle | |
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| Exercises | |
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| Reaction Diffusion, Chemotaxis, and Nonlocal Mechanisms | |
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| Simple Random Walk and Derivation of the Diffusion Equation | |
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| Reaction Diffusion Equations | |
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| Models for Animal Dispersal | |
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| Chemotaxis | |
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| Nonlocal Effects and Long Range Diffusion | |
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| Cell Potential and Energy Approach to Diffusion and Long Range Effects | |
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| Exercises | |
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| Oscillator-Generated Wave Phenomena | |
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| Belousov-Zhabotinskii Reaction Kinematic Waves | |
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| Central Pattern Generator: Experimental Facts in the Swimming of Fish | |
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| Mathematical Model for the Central Pattern Generator | |
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| Analysis of the Phase Coupled Model System | |
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| Exercises | |
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| Biological Waves: Single-Species Models | |
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| Background and the Travelling Waveform | |
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| Fisher-Kolmogoroff Equation and Propagating Wave Solutions | |
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| Asymptotic Solution and Stability of Wavefront Solutions of the Fisher-Kolmogoroff Equation | |
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| Density-Dependent Diffusion-Reaction Diffusion Models and Some Exact Solutions | |
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| Waves in Models with Multi-Steady State Kinetics: Spread and Control of an Insect Population | |
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| Calcium Waves on Amphibian Eggs: Activation Waves on Medaka Eggs | |
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| Invasion Wavespeeds with Dispersive Variability | |
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| Species Invasion and Range Expansion | |
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| Exercises | |
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| Use and Abuse of Fractals | |
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| Fractals: Basic Concepts and Biological Relevance | |
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| Examples of Fractals and Their Generation | |
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| Fractal Dimension: Concepts and Methods of Calculation | |
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| Fractals or Space-Filling? | |
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| Appendices | |
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| Phase Plane Analysis | |
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| Routh-Hurwitz Conditions, Jury Conditions, Descartes' Rule of Signs, and Exact Solutions of a Cubic | |
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| Polynomials and Conditions | |
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| Descartes' Rule of Signs | |
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| Roots of a General Cubic Polynomial | |
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| Bibliography | |
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| Index | |
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| J.D. Murray: Mathematical Biology, II: Spatial Models and Biomedical Applications | |
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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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| 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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| 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, 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 | |
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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 Condensation 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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| 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 Equation Solutions 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 (Removal) 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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| Modeling 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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| 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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| Spatial Spread of Rabies Among Foxes II: Three-Species (SIR) Model | |
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| Control Strategy Based on Wave Propagation into a Non-epidemic 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 Densitics: Quantitative Predictions for a Rabies Outbreak in England | |
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| Effect of Fox Immunity on Spatial Spread of Rabies | |
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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 | |