生物数学 第2版=MATHEMATICAL BIOLOGY SECONDPDF|Epub|txt|kindle电子书版本网盘下载

生物数学 第2版=MATHEMATICAL BIOLOGY SECONDPDF格式电子书版下载

注意：本站所有压缩包均有解压码： 点击下载压缩包解压工具

1．Continuous Population Models for Single Species1

1.1 Continuous Growth Models1

1.2 Insect Outbreak Model：Spruce Budworm4

1.3 Delay Models8

1.4 Linear Analysis of Delay Population Models：Periodic Solutions12

1.5 Delay Models in Physiology：Dynamic Diseases15

1.6 Harvesting a Single Natural Population24

1.7 Population Model with Age Distribution29

Exercises33

2．Discrete Population Models for a Single Species36

2.1 Introduction：Simple Models36

2.2 Cobwebbing：A Graphical Procedure of Solution38

2.3 Discrete Logistic Model：Chaos41

2.4 Stability,Periodic Solutions and Bifurcations47

2.5 Discrete Delay Models51

2.6 Fishery Management Model54

2.7 Ecological Implications and Caveats57

Exercises59

3．Continuous Models for Interacting Populations63

3.1 Predator-Prey Models：Lotka-Volterra Systems63

3.2 Complexity and Stability68

3.3 Realistic Predator-Prey Models70

3.4 Analysis of a Predator-Prey Model with Limit Cycle Periodic Behaviour：Parameter Domains of Stability72

3.5 Competition Models：Principle of Competitive Exclusion78

3.6 Mutualism or Symbiosis83

3.7 General Models and Some General and Cautionary Remarks85

3.8 Threshold Phenomena89

Exercises92

4．Discrete Growth Models for Interacting Populations95

4.1 Predator-Prey Models：Detailed Analysis96

4.2 Synchronized Insect Emergence：13 Year Locusts100

4.3 Biological Pest Control：General Remarks106

Exercises107

5．Reaction Kinetics109

5.1 Enzyme Kinetics：Basic Enzyme Reaction109

5.2 Michaelis-Menten Theory：Detailed Analysis and the Pseudo-Steady State Hypothesis111

5.3 Cooperative Phenomena118

5.4 Autocatalysis,Activation and Inhibition122

5.5 Multiple Steady States,Mushrooms and Isolas130

Exercises137

6．Biological Oscillators and Switches140

6.1 Motivation,History and Background140

6.2 Feedback Control Mechanisms143

6.3 Oscillations and Switches Involving Two or More Species：General Qualitative Results148

6.4 Simple Two-Species Oscillators：Parameter Domain Determination for Oscillations156

6.5 Hodgkin-Huxley Theory of Nerve Membranes：FitzHugh-Nagumo Model161

6.6 Modelling the Control of Testosterone Secretion166

Exercises175

7．Belousov-Zhabotinskii Reaction179

7.1 Belousov Reaction and the Field-Noyes（FN）Model179

7.2 Linear Stability Analysis of the FN Model and Existence of Limit Cycle Solutions183

7.3 Non-local Stability of the FN Model187

7.4 Relaxation Oscillators：Approximation for the Belousov-Zhabotinskii Reaction190

7.5 Analysis of a Relaxation Model for Limit Cycle Oscillations in the Belousov-Zhabotinskii Reaction192

Exercises199

8．Perturbed and Coupled Oscillators and Black Holes200

8.1 Phase Resetting in Oscillators200

8.2 Phase Resetting Curves204

8.3 Black Holes208

8.4 Black Holes in Real Biological Oscillators210

8.5 Coupled Oscillators：Motivation and Model System215

8.6 Singular Perturbation Analysis：Preliminary Transformation217

8.7 Singular Perturbation Analysis：Transformed System220

8.8 Singular perturbation Analysis：Two-Time Expansion223

8.9 Analysis of the Phase Shift Equation and Application to Coupled Belousov-Zhabotinskii Reactions227

Exercises231

9．Reaction Diffusion,Chemotaxis and Non-local Mechanisms232

9.1 Simple Random Walk Derivation of the Diffusion Equation232

9.2 Reaction Diffusion Equations236

9.3 Models for Insect Dispersal238

9.4 Chemotaxis241

9.5 Non-local Effects and Long Range Diffusion244

9.6 Cell Potential and Energy Approach to Diffusion249

Exercises252

10．Oscillator Generated Wave Phenomena and Central Pattern Generators254

10.1 Kinematic Waves in the Belousov-Zhabotinskii Reaction254

10.2 Central Pattern Generator：Experimental Facts in the Swimming of Fish258

10.3 Mathematical Model for the Central Pattern Generator261

10.4 Analysis of the Phase-Coupled Model System268

Exercises273

11．Biological Waves：Single Species Models274

11.1 Background and the Travelling Wave Form274

11.2 Fisher Equation and Propagating Wave Solutions277

11.3 Asymptotic Solution and Stability of Wavefront Solutions of the Fisher Equation281

11.4 Density-Dependent Diffusion Reaction Diffusion Models and Some Exact Solutions286

11.5 Waves in Models with Multi-Steady State Kinetics：The Spread and Control of an Insect Population297

11.6 Calcium Waves on Amphibian Eggs：Activation Waves on Medaka Eggs305

Exercises309

12．Biological Waves：Multi-species Reaction Diffusion Models311

12.1 Intuitive Expectations311

12.2 Waves of Pursuit and Evasion in Predator-Prey Systems315

12.3 Travelling Fronts in the Belousov-Zhabotinskii Reaction322

12.4 Waves in Excitable Media328

12.5 Travelling Wave Trains in Reaction Diffusion Systems with Oscillatory Kinetics336

12.6 Linear Stability of Wave Train Solutions of λ-ω Systems340

12.7 Spiral Waves343

12.8 Spiral Wave Solutions of λ-ω Reaction Diffusion Systems350

Exercises356

13．Travelling Waves in Reaction Diffusion Systems with Weak Diffusion：Analytical Techniques and Results360

13.1 Reaction Diffusion System with Limit Cycle Kinetics and Weak Diffusion：Model and Transformed System360

13.2 Singular Perturbation Analysis：The Phase Satisfies Burgers'Equation363

13.3 Travelling Wavetrain Solutions for Reaction Diffusion Systems with Limit Cycle Kinetics and Weak Diffusion：Comparison with Experiment367

14．Spatial Pattern Formation with Reaction/Population Interaction Diffusion Mechanisms372

14.1 Role of Pattern in Developmental Biology372

14.2 Reaction Diffusion（Turing）Mechanisms375

14.3 Linear Stability Analysis and Evolution of Spatial Pattern：General Conditions for Diffusion-Driven Instability380

14.4 Detailed Analysis of Pattern Initiation in a Reaction Diffusion Mechanism387

14.5 Dispersion Relation,Turing Space,Scale and Geometry Effects in Pattern Formation in Morphogenetic Models397

14.6 Mode Selection and the Dispersion Relation408

14.7 Pattern Generation with Single Species Models：Spatial Heterogeneity with the Spruce Budworm Model414

14.8 Spatial Patterns in Scalar Population Interaction-Reaction Diffusion Equations with Convection：Ecological Control Strategies419

14.9 Nonexistence of Spatial Patterns in Reaction Diffusion Systems：General and Particular Results424

Exercises430

15．Animal Coat Patterns and Other Practical Applications of Reaction Diffusion Mechanisms435

15.1 Mammalian Coat Patterns-‘How the Leopard Got Its Spots’436

15.2 A Pattern Formation Mechanism for Butterfly Wing Patterns448

15.3 Modelling Hair Patterns in a Whorl in Acetabularia468

16．Neural Models of Pattern Formation481

16.1 Spatial Patterning in Neural Firing with a Simple Activation Inhibition Model481

16.2 A Mechanism for Stripe Formation in the Visual Cortex489

16.3 A Model for the Brain Mechanism Underlying Visual Hallucination Patterns494

16.4 Neural Activity Model for Shell Patterns505

Exercises523

17．Mechanical Models for Generating Pattern and Form in Development525

17.1 Introduction and Background Biology525

17.2 Mechanical Model for Mesenchymal Morphogenesis528

17.3 Linear Analysis,Dispersion Relation and Pattern Formation Potential538

17.4 Simple Mechanical Models Which Generate Spatial Patterns with Complex Dispersion Relations542

17.5 Periodic Patterns of Feather Germs554

17.6 Cartilage Condensations in Limb Morphogenesis558

17.7 Mechanochemical Model for the Epidermis566

17.8 Travelling Wave Solutions of the Cytogel Model572

17.9 Formation of Microvilli579

17.10 Other Applications of Mechanochemical Models586

Exercises590

18．Evolution and Developmental Programmes593

18.1 Evolution and Morphogenesis593

18.2 Evolution and Morphogenetic Rules in Cartilage Formation in the Vertebrate Limb599

18.3 Developmental Constraints,Morphogenetic Rules and the Consequences for Evolution606

19．Epidemic Models and the Dynamics of Infectious Diseases610

19.1 Simple Epidemic Models and Practical Applications611

19.2 Modelling Venereal Diseases619

19.3 Multigroup Model for Gonorrhea and Its Control623

19.4 AIDS：Modelling the Transmission Dynamics of the Human Immunodeficiency Virus（HIV）624

19.5 Modelling the Population Dynamics of Acquired Immunity to Parasite Infection630

19.6 Age Dependent Epidemic Model and Threshold Criterion640

19.7 Simple Drug Use Epidemic Model and Threshold Analysis645

Exercises649

20．Geographic Spread of Epidemics651

20.1 Simple Model for the Spatial Spread of an Epidemic651

20.2 Spread of the Black Death in Europe 1347-1350655

20.3 The Spatial Spread of Rabies Among Foxes Ⅰ：Background and Simple Model659

20.4 The Spatial Spread of Rabies Among Foxes Ⅱ：Three Species（SIR）Model666

20.5 Control Strategy Based on Wave Propagation into a Non-epidemic Region：Estimate of Width of a Rabies Barrier681

20.6 Two-Dimensional Epizootic Fronts and Effects of Variable Fox Densities：Quantitative Predictions for a Rabies Outbreak in England689

Exercises696

Appendices697

1．Phase Plane Analysis697

2．Routh-Hurwitz Conditions,Jury Conditions,Descartes'Rule of Signs and Exact Solutions of a Cubic702

3．Hopf Bifurcation Theorem and Limit Cycles706

4．General Results for the Laplacian Operator in Bounded Domains720

Bibliography723

Index745