.

0 (hodnocen0 x )

(0.5) Půjčeno:1x 

BK

3rd ed.

Berlin : Springer, c2002

xxiii, 551 s.

ISBN 0-387-95223-3 (váz.)

Interdisciplinary applied mathematics ; 17

Obsahuje předmluvu, dodatky, rejstřík

Bibliografie: s. 513-535

Biologie - optimalizace matematická - učebnice vysokošk.

000059050

CONTENTS, VOLUME I // Preface to the Third Edition vii // Preface to the First Edition xi // 1. Continuous Population Models for Single Species 1 // 1.1 Continuous Growth Models 1 // 1.2 Insect Outbreak Model: Spruce Budworm 7 // 1.3 Delay Models 13 // 1.4 Linear Analysis of Delay Population Models: Periodic Solutions 17 // 1.5 Delay Models in Physiology: Periodic Dynamic Diseases 21 // 1.6 Harvesting a Single Natural Population 30 // 1.7 Population Model with Age Distribution 36 // Exercises 40 // 2. Discrete Population Models for a Single Species 44 // 2.1 Introduction: Simple Models 44 // 2.2 Cobwebbing: A Graphical Procedure of Solution 49 // 2.3 Discrete Logistic-Type Model: Chaos 53 // 2.4 Stability, Periodic Solutions and Bifurcations 59 // 2.5 Discrete Delay Models 62 // 2.6 Fishery Management Model 67 // 2.7 Ecological Implications and Caveats 69 // 2.8 Tumour Cell Growth 72 // Exercises 75 // 3. Models for Interacting Populations 79 // 3.1 Predator-Prey Models: Lotka-Volterra Systems 79 // 3.2 Complexity and Stability 83 // 3.3 Realistic Predator-Prey Models 86 // 3.4 Analysis of a Predator-Prey Model with Limit Cycle // Periodic Behaviour: Parameter Domains of Stability 88 // 3.5 Competition Models: Competitive Exclusion Principle 94 // 3.6 Mutualism or Symbiosis 99 // 3.7 General Models and Cautionary Remarks 101 // 3.8 Threshold Phenomena 105 // 3.9 Discrete Growth Models for Interacting Populations 109 // 3.10 Predator-Prey Models: Detailed Analysis 110 // Exercises 115 // 4. Temperature-Dependent Sex Determination (TSD) 119 // 4.1 Biological Introduction and Historical Asides on the Crocodilia 119 // 4.2 Nesting Assumptions and Simple Population Model 124 // 4.3 Age-Structured Population Model for Crocodilia 130 // 4.4 Density-Dependent Age-Structured Model Equations 133 // 4.5 Stability of the Female Population in Wet Marsh Region I 135 //

4.6 Sex Ratio and Survivorship 137 // 4.7 Temperature-Dependent Sex Determination (TSD) Versus // Genetic Sex Determination (GSD) 139 // 4.8 Related Aspects on Sex Determination 142 // Exercise 144 // 5. Modelling the Dynamics of Marital Interaction: Divorce Prediction // and Marriage Repair 146 // 5.1 Psychological Background and Data: // Gottman and Levenson Methodology 147 // 5.2 Marital Typology and Modelling Motivation 150 // 5.3 Modelling Strategy and the Model Equations 153 // 5.4 Steady States and Stability 156 // 5.5 Practical Results from the Model 164 // 5.6 Benefits, Implications and Marriage Repair Scenarios 170 // 6. Reaction Kinetics 175 // 6.1 Enzyme Kinetics: Basic Enzyme Reaction 175 // 6.2 Transient Time Estimates and Nondimensionalisation 178 // 6.3 Michaelis-Menten Quasi-Steady State Analysis 181 // 6.4 Suicide Substrate Kinetics 188 // 6.5 Cooperative Phenomena 197 // 6.6 Autocatalysis, Activation and Inhibition 201 // 6.7 Multiple Steady States, Mushrooms and Isolas 208 // Exercises 215 // 7. Biological Oscillators and Switches 218 // 7.1 Motivation, Brief History and Background 218 // 7.2 Feedback Control Mechanisms 221 // 7.3 Oscillators and Switches with Two or More Species: // General Qualitative Results 226 // 7.4 Simple Two-Species Oscillators: Parameter Domain // Determination for Oscillations 234 // Table of Contents, Volume I xvii // 7.5 Hodgkin-Huxley Theory of Nerve Membranes: FitzHugh-Nagumo Model 239 // 7.6 Modelling the Control of Testosterone Secretion and Chemical Castration 244 // Exercises 253 // 8. BZ Oscillating Reactions 257 // 8.1 Belousov Reaction and the Field-Körös-Noyes (FKN) Model 257 // 8.2 Linear Stability Analysis of the FKN Model and Existence of Limit Cycle Solutions 261 // 8.3 Nonlocal Stability of the FKN Model 265 // 8.4 Relaxation Oscillators: Approximation for the Belousov-Zhabotinskii Reaction 268 //

8.5 Analysis of a Relaxation Model for Limit Cycle Oscillations // in the Belousov-Zhabotinskii Reaction 271 // Exercises 277 // 9. Perturbed and Coupled Oscillators and Black Holes 278 // 9.1 Phase Resetting in Oscillators 278 // 9.2 Phase Resetting Curves 282 // 9.3 Black Holes 286 // 9.4 Black Holes in Real Biological Oscillators 288 // 9.5 Coupled Oscillators: Motivation and Model System 293 // 9.6 Phase Locking of Oscillations: Synchronisation in Fireflies 295 // 9.7 Singular Perturbation Analysis: Preliminary Transformation 299 // 9.8 Singular Perturbation Analysis: Transformed System 302 // 9.9 Singular Perturbation Analysis: Two-Time Expansion 305 // 9.10 Analysis of the Phase Shift Equation and Application // to Coupled Belousov-Zhabotinskii Reactions 310 // Exercises 313 // 10. Dynamics of Infectious Diseases 315 // 10.1 Historical Aside on Epidemics 315 // 10.2 Simple Epidemic Models and Practical Applications 319 // 10.3 Modelling Venereal Diseases 327 // 10.4 Multi-Group Model for Gonorrhea and Its Control 331 // 10.5 AIDS: Modelling the Transmission Dynamics of the Human // Immunodeficiency Virus (HIV) 333 // 10.6 HIV: Modelling Combination Drug Therapy 341 // 10.7 Delay Model for HIV Infection with Drug Therapy 350 // 10.8 Modelling the Population Dynamics of Acquired Immunity to // Parasite Infection 351 // 10.9 Age-Dependent Epidemic Model and Threshold Criterion 361 // 10.10 Simple Drug Use Epidemic Model and Threshold Analysis 365 // 10.11 Bovine Tuberculosis Infection in Badgers and Cattle 369 // 10.12 Modelling Control Strategies for Bovine Tuberculosis // in Badgers and Cattle 379 // Exercises 393 // 11. Reaction Diffusion, Chemotaxis, and Nonlocal Mechanisms 395 // 11.1 Simple Random Walk and Derivation of the Diffusion Equation 395 // 11.2 Reaction Diffusion Equations 399 // 11.3 Models for Animal Dispersal 402 // 11.4 Chemotaxis 405 //

11.5 Nonlocal Effects and Long Range Diffusion 408 // 11.6 Cell Potential and Energy Approach to Diffusion // and Long Range Effects 413 // Exercises 416 // 12. Oscillator-Generated Wave Phenomena 418 // 12.1 Belousov-Zhabotinskii Reaction Kinematic Waves 418 // 12.2 Central Pattem Generator: Experimental Facts in the Swimming of Fish 422 // 12.3 Mathematical Model for the Central Pattem Generator 424 // 12.4 Analysis of the Phase Coupled Model System 431 // Exercises 436 // 13. Biological Waves: Single-Species Models 437 // 13.1 Background and the Travelling Waveform 437 // 13.2 Fisher-Kolmogoroff Equation and Propagating Wave Solutions 439 // 13.3 Asymptotic Solution and Stability of Wavefront Solutions of the Fisher-Kolmogoroff Equation 444 // 13.4 Density-Dependent Diffusion-Reaction Diffusion Models and Some Exact Solutions 449 // 13.5 Waves in Models with Multi-Steady State Kinetics: Spread and Control of an Insect Population 460 // 13.6 Calcium Waves on Amphibian Eggs: Activation Waves on Medaka Eggs 467 // 13.7 Invasion Wavespeeds with Dispersive Variability 471 // 13.8 Species Invasion and Range Expansion 478 // Exercises 482 // 14. Use and Abuse of Fractals 484 // 14.1 Fractals: Basic Concepts and Biological Relevance 484 // 14.2 Examples of Fractals and Their Generation 487 // 14.3 Fractal Dimension: Concepts and Methods of Calculation 490 // 14.4 Fractals or Space-Filling? 496 // Appendices 501 // A. Phase Plane Analysis 501 // ?. Routh-Hurwitz Conditions, Jury Conditions, Descartes’ // Rule of Signs, and Exact Solutions of a Cubic 507 // B.l Polynomials and Conditions 507 // B.2 Descartes’Rule of Signs 509 // B.3 Roots of a General Cubic Polynomial 510 // Bibliography 513 // Index 537