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図書

図書
J.D. Murray
出版情報: New York ; Berlin : Springer, c2003  xxv, 811 p. ; 25 cm
シリーズ名: Interdisciplinary applied mathematics ; v. 18 . Mathematical biology ; 2
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Preface to the Third Edition
Preface to the First Edition
Multi-Species Waves and Practical Applications / 1.:
Intuitive Expectations / 1.1:
Waves of Pursuit and Evasion in Predator-Prey Systems / 1.2:
Competition Model for the Spatial Spread of the Grey Squirrel in Britain / 1.3:
Spread of Genetically Engineered Organisms / 1.4:
Travelling Fronts in the Belousov-Zhabotinskii Reaction / 1.5:
Waves in Excitable Media / 1.6:
Travelling Wave Trains in Reaction Diffusion Systems with Oscillatory Kinetics / 1.7:
Spiral Waves / 1.8:
Spiral Wave Solutions of [lambda]-[omega] Reaction Diffusion Systems / 1.9:
Exercises
Spatial Pattern Formation with Reaction Diffusion Systems / 2.:
Role of Pattern in Biology / 2.1:
Reaction Diffusion (Turing) Mechanisms / 2.2:
General Conditions for Diffusion-Driven Instability: Linear Stability Analysis and Evolution of Spatial Pattern / 2.3:
Detailed Analysis of Pattern Initiation in a Reaction Diffusion Mechanism / 2.4:
Dispersion Relation, Turing Space, Scale and Geometry Effects in Pattern Formation Models / 2.5:
Mode Selection and the Dispersion Relation / 2.6:
Pattern Generation with Single-Species Models: Spatial Heterogeneity with the Spruce Budworm Model / 2.7:
Spatial Patterns in Scalar Population Interaction Diffusion Equations with Convection: Ecological Control Strategies / 2.8:
Nonexistence of Spatial Patterns in Reaction Diffusion Systems: General and Particular Results / 2.9:
Animal Coat Patterns and Other Practical Applications of Reaction Diffusion Mechanisms / 3.:
Mammalian Coat Patterns--'How the Leopard Got Its Spots' / 3.1:
Teratologies: Examples of Animal Coat Pattern Abnormalities / 3.2:
A Pattern Formation Mechanism for Butterfly Wing Patterns / 3.3:
Modelling Hair Patterns in a Whorl in Acetabularia / 3.4:
Pattern Formation on Growing Domains: Alligators and Snakes / 4.:
Stripe Pattern Formation in the Alligator: Experiments / 4.1:
Modelling Concepts: Determining the Time of Stripe Formation / 4.2:
Stripes and Shadow Stripes on the Alligator / 4.3:
Spatial Patterning of Teeth Primordia in the Alligator: Background and Relevance / 4.4:
Biology of Tooth Initiation / 4.5:
Modelling Tooth Primordium Initiation: Background / 4.6:
Model Mechanism for Alligator Teeth Patterning / 4.7:
Results and Comparison with Experimental Data / 4.8:
Prediction Experiments / 4.9:
Concluding Remarks on Alligator Tooth Spatial Patterning / 4.10:
Pigmentation Pattern Formation on Snakes / 4.11:
Cell-Chemotaxis Model Mechanism / 4.12:
Simple and Complex Snake Pattern Elements / 4.13:
Propagating Pattern Generation with the Cell-Chemotaxis System / 4.14:
Bacterial Patterns and Chemotaxis / 5.:
Background and Experimental Results / 5.1:
Model Mechanism for E. coli in the Semi-Solid Experiments / 5.2:
Liquid Phase Model: Intuitive Analysis of Pattern Formation / 5.3:
Interpretation of the Analytical Results and Numerical Solutions / 5.4:
Semi-Solid Phase Model Mechanism for S. typhimurium / 5.5:
Linear Analysis of the Basic Semi-Solid Model / 5.6:
Brief Outline and Results of the Nonlinear Analysis / 5.7:
Simulation Results, Parameter Spaces and Basic Patterns / 5.8:
Numerical Results with Initial Conditions from the Experiments / 5.9:
Swarm Ring Patterns with the Semi-Solid Phase Model Mechanism / 5.10:
Branching Patterns in Bacillus subtilis / 5.11:
Mechanical Theory for Generating Pattern and Form in Development / 6.:
Introduction, Motivation and Background Biology / 6.1:
Mechanical Model for Mesenchymal Morphogenesis / 6.2:
Linear Analysis, Dispersion Relation and Pattern Formation Potential / 6.3:
Simple Mechanical Models Which Generate Spatial Patterns with Complex Dispersion Relations / 6.4:
Periodic Patterns of Feather Germs / 6.5:
Cartilage Condensations in Limb Morphogenesis and Morphogenetic Rules / 6.6:
Embryonic Fingerprint Formation / 6.7:
Mechanochemical Model for the Epidermis / 6.8:
Formation of Microvilli / 6.9:
Complex Pattern Formation and Tissue Interaction Models / 6.10:
Evolution, Morphogenetic Laws, Developmental Constraints and Teratologies / 7.:
Evolution and Morphogenesis / 7.1:
Evolution and Morphogenetic Rules in Cartilage Formation in the Vertebrate Limb / 7.2:
Teratologies (Monsters) / 7.3:
Developmental Constraints, Morphogenetic Rules and the Consequences for Evolution / 7.4:
A Mechanical Theory of Vascular Network Formation / 8.:
Biological Background and Motivation / 8.1:
Cell-Extracellular Matrix Interactions for Vasculogenesis / 8.2:
Parameter Values / 8.3:
Analysis of the Model Equations / 8.4:
Network Patterns: Numerical Simulations and Conclusions / 8.5:
Epidermal Wound Healing / 9.:
Brief History of Wound Healing / 9.1:
Biological Background: Epidermal Wounds / 9.2:
Model for Epidermal Wound Healing / 9.3:
Nondimensional Form, Linear Stability and Parameter Values / 9.4:
Numerical Solution for the Epidermal Wound Repair Model / 9.5:
Travelling Wave Solutions for the Epidermal Model / 9.6:
Clinical Implications of the Epidermal Wound Model / 9.7:
Mechanisms of Epidermal Repair in Embryos / 9.8:
Actin Alignment in Embryonic Wounds: A Mechanical Model / 9.9:
Mechanical Model with Stress Alignment of the Actin Filaments in Two Dimensions / 9.10:
Dermal Wound Healing / 10.:
Background and Motivation--General and Biological / 10.1:
Logic of Wound Healing and Initial Models / 10.2:
Brief Review of Subsequent Developments / 10.3:
Model for Fibroblast-Driven Wound Healing: Residual Strain and Tissue Remodelling / 10.4:
Solutions of the Model Equations and Comparison with Experiment / 10.5:
Wound Healing Model of Cook (1995) / 10.6:
Matrix Secretion and Degradation / 10.7:
Cell Movement in an Oriented Environment / 10.8:
Model System for Dermal Wound Healing with Tissue Structure / 10.9:
One-Dimensional Model for the Structure of Pathological Scars / 10.10:
Open Problems in Wound Healing / 10.11:
Concluding Remarks on Wound Healing / 10.12:
Growth and Control of Brain Tumours / 11.:
Medical Background / 11.1:
Basic Mathematical Model of Glioma Growth and Invasion / 11.2:
Tumour Spread In Vitro: Parameter Estimation / 11.3:
Tumour Invasion in the Rat Brain / 11.4:
Tumour Invasion in the Human Brain / 11.5:
Modelling Treatment Scenarios: General Comments / 11.6:
Modelling Tumour Resection in Homogeneous Tissue / 11.7:
Analytical Solution for Tumour Recurrence After Resection / 11.8:
Modelling Surgical Resection with Brain Tissue Heterogeneity / 11.9:
Modelling the Effect of Chemotherapy on Tumour Growth / 11.10:
Modelling Tumour Polyclonality and Cell Mutation / 11.11:
Neural Models of Pattern Formation / 12.:
Spatial Patterning in Neural Firing with a Simple Activation-Inhibition Model / 12.1:
A Mechanism for Stripe Formation in the Visual Cortex / 12.2:
A Model for the Brain Mechanism Underlying Visual Hallucination Patterns / 12.3:
Neural Activity Model for Shell Patterns / 12.4:
Shamanism and Rock Art / 12.5:
Geographic Spread and Control of Epidemics / 13.:
Simple Model for the Spatial Spread of an Epidemic / 13.1:
Spread of the Black Death in Europe 1347-1350 / 13.2:
Brief History of Rabies: Facts and Myths / 13.3:
The Spatial Spread of Rabies Among Foxes I: Background and Simple Model / 13.4:
The Spatial Spread of Rabies Among Foxes II: Three-Species (SIR) Model / 13.5:
Control Strategy Based on Wave Propagation into a Nonepidemic Region: Estimate of Width of a Rabies Barrier / 13.6:
Analytic Approximation for the Width of the Rabies Control Break / 13.7:
Two-Dimensional Epizootic Fronts and Effects of Variable Fox Densities: Quantitative Predictions for a Rabies Outbreak in England / 13.8:
Effect of Fox Immunity on the Spatial Spread of Rabies / 13.9:
Wolf Territoriality, Wolf-Deer Interaction and Survival / 14.:
Introduction and Wolf Ecology / 14.1:
Models for Wolf Pack Territory Formation: Single Pack--Home Range Model / 14.2:
Multi-Wolf Pack Territorial Model / 14.3:
Wolf-Deer Predator-Prey Model / 14.4:
Concluding Remarks on Wolf Territoriality and Deer Survival / 14.5:
Coyote Home Range Patterns / 14.6:
Chippewa and Sioux Intertribal Conflict c1750-1850 / 14.7:
Appendix
General Results for the Laplacian Operator in Bounded Domains / A.:
Bibliography
Index
Preface to the Third Edition
Preface to the First Edition
Multi-Species Waves and Practical Applications / 1.:
2.

図書

図書
Kenneth P. Burnham, David R. Anderson
出版情報: New York : Springer, c1998  xix, 353 p. ; 24 cm
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3.

図書

図書
Bruce J. West
出版情報: Berlin ; Tokyo : Springer-Verlag, c1985  viii, 204 p. ; 25 cm
シリーズ名: Lecture notes in biomathematics ; 62
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4.

図書

図書
Commentary and reprints by Edward H. Kerner
出版情報: New York : Gordon and Breach, [1972]  xi, 167 p ; 24 cm
シリーズ名: International science review series ; v. 12
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5.

図書

図書
Narendra S. Goel, Nira Richter-Dyn
出版情報: New York : Academic Press, 1974  x, 269 p. ; 24 cm
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6.

図書

図書
D. Brown and P. Rothery
出版情報: Chichester, England ; New York : Wiley, c1993  xix, 688 p. ; 25 cm
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7.

図書

図書
Edward Beltrami
出版情報: Boston : Jones and Bartlett Publishers, c1993  xiii, 197 p. ; 24 cm
シリーズ名: Jones and Bartlett books in mathematics
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8.

図書

図書
Norman MacDonald
出版情報: Berlin ; New York : Springer-Verlag, 1978  vi, 112 p. ; 25 cm
シリーズ名: Lecture notes in biomathematics ; 27
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9.

図書

図書
Paul C. Fife
出版情報: Berlin ; New York : Springer-Verlag, 1979  iv, 185 p. ; 25 cm
シリーズ名: Lecture notes in biomathematics ; 28
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10.

図書

図書
Harvey J. Gold
出版情報: New York : Wiley, c1977  xv, 357 p. ; 24 cm
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