An Introduction to Mathematical Biology... | WHSmith Books
An Introduction to Mathematical Biology

An Introduction to Mathematical Biology

By: Linda J. S. Allen (author)Hardback

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Description

For advanced undergraduate and beginning graduate courses on Modeling offered in departments of Mathematics. This text introduces a variety of mathematical models for biological systems, and presents the mathematical theory and techniques useful in analyzing those models. Material is organized according to the mathematical theory rather than the biological application. Undergraduate courses in calculus, linear algebra, and differential equations are assumed.

Contents

Preface xi1 LINEAR DIFFERENCE EQUATIONS, THEORY, AND EXAMPLES 11.1 Introduction 11.2 Basic Definitions and Notation 21.3 First-Order Equations 61.4 Second-Order and Higher-Order Equations 81.5 First-Order Linear Systems 141.6 An Example: Leslie's Age-Structured Model 181.7 Properties of the Leslie Matrix 201.8 Exercises for Chapter 1 281.9 References for Chapter 1 331.10 Appendix for Chapter 1 34 1.10.1 Maple Program:Turtle Model 34 1.10.2 MATLAB (R) Program:Turtle Model 342 NONLINEAR DIFFERENCE EQUATIONS, THEORY, AND EXAMPLES 362.1 Introduction 362.2 Basic Definitions and Notation 372.3 Local Stability in First-Order Equations 402.4 Cobwebbing Method for First-Order Equations 452.5 Global Stability in First-Order Equations 462.6 The Approximate Logistic Equation 522.7 Bifurcation Theory 55 2.7.1 Types of Bifurcations 56 2.7.2 Liapunov Exponents 602.8 Stability in First-Order Systems 622.9 Jury Conditions 672.10 An Example: Epidemic Model 692.11 Delay Difference Equations 732.12 Exercises for Chapter 2 762.13 References for Chapter 2 822.14 Appendix for Chapter 2 84 2.14.1 Proof of Theorem 2.1 84 2.14.2 A Definition of Chaos 86 2.14.3 Jury Conditions (Schur-Cohn Criteria) 86 2.14.4 Liapunov Exponents for Systems of Difference Equations 87 2.14.5 MATLAB Program: SIR Epidemic Model 883 BIOLOGICAL APPLICATIONS OF DIFFERENCE EQUATIONS 893.1 Introduction 893.2 Population Models 903.3 Nicholson-Bailey Model 923.4 Other Host-Parasitoid Models 963.5 Host-Parasite Model 983.6 Predator-Prey Model 993.7 Population Genetics Models 1033.8 Nonlinear Structured Models 110 3.8.1 Density-Dependent Leslie Matrix Models 110 3.8.2 Structured Model for Flour Beetle Populations 116 3.8.3 Structured Model for the Northern Spotted Owl 118 3.8.4 Two-Sex Model 1213.9 Measles Model with Vaccination 1233.10 Exercises for Chapter 3 1273.11 References for Chapter 3 1343.12 Appendix for Chapter 3 138 3.12.1 Maple Program: Nicholson-Bailey Model 138 3.12.2 Whooping Crane Data 138 3.12.3 Waterfowl Data 1394 LINEAR DIFFERENTIAL EQUATIONS: THEORY AND EXAMPLES 1414.1 Introduction 1414.2 Basic Definitions and Notation 1424.3 First-Order Linear Differential Equations 1444.4 Higher-Order Linear Differential Equations 145 4.4.1 Constant Coefficients 1464.5 Routh-Hurwitz Criteria 1504.6 Converting Higher-Order Equations to First-OrderSystems 1524.7 First-Order Linear Systems 154 4.7.1 Constant Coefficients 1554.8 Phase-Plane Analysis 1574.9 Gershgorin's Theorem 1624.10 An Example: Pharmacokinetics Model 1634.11 Discrete and Continuous Time Delays 1654.12 Exercises for Chapter 4 1694.13 References for Chapter 4 1724.14 Appendix for Chapter 4 173 4.14.1 Exponential of a Matrix 173 4.14.2 Maple Program: Pharmacokinetics Model 1755 NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS: THEORY AND EXAMPLES 1765.1 Introduction 1765.2 Basic Definitions and Notation 1775.3 Local Stability in First-Order Equations 180 5.3.1 Application to Population Growth Models 1815.4 Phase Line Diagrams 1845.5 Local Stability in First-Order Systems 1865.6 Phase Plane Analysis 1915.7 Periodic Solutions 194 5.7.1 Poincare-Bendixson Theorem 194 5.7.2 Bendixson's and Dulac's Criteria 1975.8 Bifurcations 199 5.8.1 First-Order Equations 200 5.8.2 Hopf Bifurcation Theorem 2015.9 Delay Logistic Equation 2045.10 Stability Using Qualitative Matrix Stability 2115.11 Global Stability and Liapunov Functions 2165.12 Persistence and Extinction Theory 2215.13 Exercises for Chapter 5 2245.14 References for Chapter 5 2325.15 Appendix for Chapter 5 234 5.15.1 Subcritical and Supercritical Hopf Bifurcations 234 5.15.2 Strong Delay Kernel 2356 BIOLOGICAL APPLICATIONS OF DIFFERENTIAL EQUATIONS 2376.1 Introduction 2376.2 Harvesting a Single Population 2386.3 Predator-Prey Models 2406.4 Competition Models 248 6.4.1 Two Species 248 6.4.2 Three Species 2506.5 Spruce Budworm Model 2546.6 Metapopulation and Patch Models 2606.7 Chemostat Model 263 6.7.1 Michaelis-Menten Kinetics 263 6.7.2 Bacterial Growth in a Chemostat 2666.8 Epidemic Models 271 6.8.1 SI, SIS, and SIR Epidemic Models 271 6.8.2 Cellular Dynamics of HIV 2766.9 Excitable Systems 279 6.9.1 Van der Pol Equation 279 6.9.2 Hodgkin-Huxley and FitzHugh-Nagumo Models 2806.10 Exercises for Chapter 6 2836.11 References for Chapter 6 2926.12 Appendix for Chapter 6 296 6.12.1 Lynx and Fox Data 296 6.12.2 Extinction in Metapopulation Models 2967 PARTIAL DIFFERENTIAL EQUATIONS: THEORY, EXAMPLES, AND APPLICATIONS 2997.1 Introduction 2997.2 Continuous Age-Structured Model 300 7.2.1 Method of Characteristics 302 7.2.2 Analysis of the Continuous Age-Structured Model 3067.3 Reaction-Diffusion Equations 3097.4 Equilibrium and Traveling Wave Solutions 3167.5 Critical Patch Size 3197.6 Spread of Genes and Traveling Waves 3217.7 Pattern Formation 3257.8 Integrodifference Equations 3307.9 Exercises for Chapter 7 3317.10 References for Chapter 7 336Index 339

Product Details

  • ISBN13: 9780130352163
  • Format: Hardback
  • Number Of Pages: 368
  • ID: 9780130352163
  • weight: 894
  • ISBN10: 0130352160

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