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| Preface | |
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| Linear Difference Equations, Theory, And Examples | |
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| Introduction | |
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| Basic Definitions and Notation | |
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| First-Order Equations | |
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| Second-Order and Higher-Order Equations | |
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| First-Order Linear Systems | |
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| An Example: Leslies Age-Structured Model | |
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| Properties of the Leslie Matrix | |
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| Exercises for Chapter 1 | |
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| References for Chapter 1 | |
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| Appendix for Chapter 1 | |
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| Maple Program:Turtle Model | |
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| MATLAB? Program:Turtle Model | |
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| Nonlinear Difference Equations, Theory, And Examples | |
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| Introduction | |
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| Basic Definitions and Notation | |
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| Local Stability in First-Order Equations | |
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| Cobwebbing Method for First-Order Equations | |
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| Global Stability in First-Order Equations | |
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| The Approximate Logistic Equation | |
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| Bifurcation Theory | |
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| Types of Bifurcations | |
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| Liapunov Exponents | |
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| Stability in First-Order Systems | |
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| Jury Conditions | |
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| An Example: Epidemic Model | |
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| Delay Difference Equations | |
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| Exercises for Chapter 2 | |
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| References for Chapter 2 | |
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| Appendix for Chapter 2 | |
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| Proof of Theorem 2.1 | |
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| A Definition of Chaos | |
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| Jury Conditions (Schur-Cohn Criteria) | |
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| Liapunov Exponents for Systems of Difference Equations | |
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| MATLAB Program: SIR Epidemic Model | |
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| Biological Applications Of Difference Equations | |
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| Introduction | |
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| Population Models | |
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| Nicholson-Bailey Model | |
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| Other Host-Parasitoid Models | |
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| Host-Parasite Model | |
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| Predator-Prey Model | |
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| Population Genetics Models | |
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| Nonlinear Structured Models | |
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| Density-Dependent Leslie Matrix Models | |
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| Structured Model for Flour Beetle Populations | |
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| Structured Model for the Northern Spotted Owl | |
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| Two-Sex Model | |
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| Measles Model with Vaccination | |
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| Exercises for Chapter 3 | |
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| References for Chapter 3 | |
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| Appendix for Chapter 3 | |
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| Maple Program: Nicholson-Bailey Model | |
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| Whooping Crane Data | |
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| Waterfowl Data | |
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| Linear Differential Equations: Theory And Examples | |
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| Introduction 141 | |
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| Basic Definitions and Notation 142 | |
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| First-Order Linear Differential Equations 144 | |
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| Higher-Order Linear Differential Equations 145 | |
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| Constant Coefficients 146 | |
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| Routh-Hurwitz Criteria 150 | |
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| Converting Higher-Order Equations to First-OrderSystems 152 | |
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| First-Order Linear Systems 154 | |
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| Constant Coefficients 155 | |
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| Phase-Plane Analysis 157 | |
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| Gershgorins Theorem 162 | |
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| An Example: Pharmacokinetics Model | |
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| Discrete and Continuous Time Delays | |
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| Exercises for Chapter 4 | |
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| References for Chapter 4 | |
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| Appendix for Chapte | |