生物数学 第2卷 英文2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

生物数学 第2卷 英文PDF格式电子书版下载

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1．Multi-Species Waves and Practical Applications1

1.1 Intuitive Expectations1

1.2 Waves of Pursuit and Evasion in Predator-Prey Systems5

1.3 Competition Model for the Spatial Spread of the Grey Squirrel in Britain12

1.4 Spread of Genetically Engineered Organisms18

1.5 Travelling Fronts in the Belousov-Zhabotinskii Reaction35

1.6 Waves in Excitable Media41

1.7 Travelling Wave Trains in Reaction Diffusion Systems with Oscillatory Kinetics49

1.8 Spiral Waves54

1.9 Spiral Wave Solutions of λ-ωReaction Diffusion Systems61

Exercises67

2．Spatial Pattern Formation with Reaction Diffusion Systems71

2.1 Role of Pattern in Biology71

2.2 Reaction Diffusion(Turing)Mechanisms75

2.3 General Conditions for Diffusion-Driven Instability:Linear Stability Analysis and Evolution of Spatial Pattern82

2.4 Detailed Analysis of Pattern Initiation in a Reaction Diffusion Mechanism90

2.5 Dispersion Relation,Turing Space,Scale and Geometry Effects in Pattern Formation Models103

2.6 Mode Selection and the Dispersion Relation113

2.7 Pattern Generation with Single-Species Models:Spatial Heterogeneity with the Spruce Budworm Model120

2.8 Spatial Patterns in Scalar Population Interaction Diffusion Equations with Convection:Ecological Control Strategies125

2.9 Nonexistence of Spatial Patterns in Reaction Difrusion Systems:General and Particular Results130

Exercises135

3．Animal Coat Patterns and Other Practical Applications of Reaction Diffusion Mechanisms141

3.1 Mammalian Coat Patterns—'How the Leopard Got Its Spots'142

3.2 Teratologies:Examples of Animal Coat Pattern Abnormalities156

3.3 A Pattern Formation Mechanism for Butterfly Wing Patterns161

3.4 Modelling Hair Patternsin a Whorl in Acetabularia180

4．Pattern Formation on Growing Domains:Alligators and Snakes192

4.1 Stripe Pattern Formation in the Alligator:Experiments193

4.2 Modelling Concepts:Determining the Time of Stripe Formation196

4.3 Stripes and Shadow Stripes on the Alligator200

4.4 Spatial Patterning of Teeth Primordia in the Alligator:Background and Relevance205

4.5 Biology of Tooth Initiation207

4.6 Modelling Tooth Primordium Initiation:Background213

4.7 Model Mechanism for Alligator Teeth Patterning215

4.8 Results and Comparison with Experimental Data224

4.9 Prediction Experiments228

4.10 Concluding Remarks on Alligator Tooth Spatial Patterning232

4.11 Pigmentation Pattern Formation on Snakes234

4.12 Cell-Chemotaxis Model Mechanism238

4.13 Simple and Complex Snake Pattern Elements241

4.14 Propagating Pattern Generation with the Cell-Chemotaxis System248

5．Bacterial Patterns and Chemotaxis253

5.1 Background and Experimental Results253

5.2 Model Mechanism for E. coli in the Semi-Solid Experiments260

5.3 Liquid Phase Model:Intuitive Analysis of Pattern Formation267

5.4 Interpretation of the Analytical Results and Numerical Solutions274

5.5 Semi-Solid Phase Model Mechanism for S. typhimurium279

5.6 Linear Analysis of the Basic Semi-Solid Model281

5.7 Brief Outline and Results of the Nonlinear Analysis287

5.8 Simulation Results,Parameter Spaces and Basic Patterns292

5.9 Numerical Results with Initial Conditions from the Experiments297

5.10 Swarm Ring Patterns with the Semi-Solid Phase Model Mechanism299

5.11 Branching Patterns in Bacillus subtilis306

6．Mechanical Theory for Generating Pattern and Form in Development311

6.1 Introduction,Motivation and Background Biology311

6.2 Mechanical Model for Mesenchymal Morphogenesis319

6.3 Linear Analysis,Dispersion Relation and Pattern Formation Potentiai330

6.4 Simple Mechanical Models Which Generate Spatial Patterns with Complex Dispersion Relations334

6.5 Periodic Patterns of Feather Germs345

6.6 Cartilage Condensations in Limb Morphogenesis and Morphogenetic Rules350

6.7 Embryonic Fingerprint Formation358

6.8 Mechanochemical Model for the Epidermis367

6.9 Formation of Microvilli374

6.10 Complex Pattern Formation and Tissue Interaction Models381

Exercises394

7．Evolution,Morphogenetic Laws,Developmental Constraints and Teratologies396

7.1 Evolution and Morphogenesis396

7.2 Evolution and Morphogenetic Rules in Cartilage Formation in the Vertebrate Limb402

7.3 Teratologies(Monsters)407

7.4 Developmental Constraints,Morphogenetic Rules and the Consequences for Evolution411

8．A Mechanical Theory of Vascular Network Formation416

8.1 Biological Background and Motivation416

8.2 Cell-Extracellular Matrix Interactions for Vasculogenesis417

8.3 Parameter Values425

8.4 Analysis of the Model Equations427

8.5 Network Patterns:Numerical Simulations and Conclusions433

9．Epidermal Wound Healing441

9.1 Brief History of Wound Healing441

9.2 Biological Background:Epidermal Wounds444

9.3 Model for Epidermal Wound Healing447

9.4 Nondimensional Form,Linear Stability and Parameter Values450

9.5 Numerical Solution for the Epidermal Wound Repair Model451

9.6 Travelling Wave Solutions for the Epidermal Model454

9.7 Clinical Implications of the Epidermal Wound Model461

9.8 Mechanisms of Epidermal Repair in Embryos468

9.9 Actin Alignment in Embryonic Wounds:A Mechanical Model471

9.10 Mechanical Model with Stress Alignment of the Actin Filaments in Two Dimensions482

10．Dermal Wound Healing491

10.1 Background and Motivation—General and Biological491

10.2 Logic of Wound Healing and Initial Models495

10.3 Brief Review of Subsequent Developments500

10.4 Model for Fibroblast-Driven Wound Healing:Residual Strain and Tissue Remodelling503

10.5 Solutions of the Model Equations and Comparison with Experiment507

10.6 Wound Healing Model of Cook(1995)511

10.7 Matrix Secretion and Degradation515

10.8 CellMovement in an Oriented Environment518

10.9 Model System for Dermal Wound Healing with Tissue Structure521

10.10 One-Dimensional Model for the Structure of Pathological Scars526

10.11 Open Problems in Wound Healing530

10.12 Concluding Remarks on Wound Healing533

11．Growthand Control of Brain Tumours536

11.1 Medical Background538

11.2 Basic Mathematical Model of Glioma Growth and Invasion542

11.3 Tumour Spread In Vitro:Parameter Estimation550

11.4 Tumour Invasionin the Rat Brain559

11.5 Tumour Invasion in the Human Brain563

11.6 Modelling Treatment Scenarios:General Comments579

11.7 Modelling Tumour Resection in Homogeneous Tissue580

11.8 Analytical Solution for Tumour Recurrence After Resection584

11.9 Modelling Surgical Resection with Brain Tissue Heterogeneity588

11.10 Modelling the Effect of Chemotherapy on Tumour Growth594

11.11 Modelling Tumour Polyclonality and Cell Mutation605

12．Neural Models of Pattern Formation614

12.1 Spatial Patterning in Neural Firng with a Simple Activation-Inhibition Model614

12.2 AMechanism for Stripe Formation in the Visual Cortex622

12.3 A Model for the Brain Mechanism Underlying Visual Hallucination Patterns627

12.4 Neural Activity Model for Shell Patterns638

12.5 Shamanism and Rock Art655

Exercises659

13．Geographic Spread and Control of Epidemics661

13.1 Simple Model for the Spatial Spread of an Epidemic661

13.2 Spread ofthe BlackDeath in Europe 1347-1350664

13.3 Brief History of Rabies:Facts and Myths669

13.4 The Spatial Spread of Rabies Among Foxes Ⅰ:Background and Simple Model673

13.5 The Spatial Spread of Rabies Among Foxes Ⅱ:Three-Species(SIR) Model681

13.6 Control Strategy Based on Wave Propagation into a Nonepidemic Region:Estimate of Width of a Rabies Barrier696

13.7 Analytic Approximation for the Width of the Rabies Control Break700

13.8 Two-Dimensional Epizootic Fronts and Effects of Variable Fox Densities:Quantitative Predictions for a Rabies Outbreak in England704

13.9 Effect of Fox Immunity on the Spatial Spread of Rabies710

Exercises720

14．Wolf Territoriality,Wolf-Deer Interaction and Survival722

14.1 Introduction and Wolf Ecology722

14.2 Models for Wolf Pack Territory Formation:Single Pack—Home Range Model729

14.3 Multi-Wolf Pack Territorial Model734

14.4 Wolf-Deer Predator-Prey Model745

14.5 Concluding Remarks on Wolf Territoriality and Deer Survival751

14.6 Coyote Home Range Patterns753

14.7 Chippewa and Sioux Intertribal Conflict c1750-1850754

Appendix757

A．General Results for the Laplacian Operator in Bounded Domains757

Bibliography761

Index791