| Description |
1 online resource (339 p.) |
| Series |
Chapman and Hall/CRC Mathematical Biology Ser |
|
Chapman and Hall/CRC Mathematical Biology Ser
|
| Contents |
Cover -- Half Title -- Series Page -- Title Page -- Copyright Page -- Dedication -- Table of Contents -- ACKNOWLEDGMENTS -- FOR PROFESSORS AND STUDENTS -- AUTHORS -- SECTION I: Introduction to Modeling -- CHAPTER 1 Mathematical Modeling -- 1.1 WHAT YOU SHOULD KNOW ABOUT THIS CHAPTER -- 1.2 THE MODELING CYCLE -- 1.2.1 Step 1: Translation into Mathematics -- 1.2.1.1 Choosing Variables and Parameters -- 1.2.1.2 Simplifying Assumptions -- 1.2.1.3 Parameterization -- 1.2.2 Step 2: Model Analysis -- 1.2.3 Step 3: Back-Translation -- 1.2.3.1 Model Selection and Validation |
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1.2.3.2 Test of Model Predictions -- 1.2.4 Step 4: Revising Model Assumptions -- 1.3 BIOLOGY -- 1.3.1 Ecology -- 1.4 MATHEMATICS -- 1.5 STATISTICS -- 1.6 EPISTEMOLOGY: HOW WE KNOW -- 1.7 EXERCISES -- BIBLIOGRAPHY -- CHAPTER 2 Avian Bone Growth: A Case Study -- 2.1 WHAT YOU SHOULD KNOW ABOUT THIS CHAPTER -- 2.2 SCIENTIFIC PROBLEM -- 2.2.1 Data -- 2.3 TRANSLATION INTO MATHEMATICS -- 2.3.1 Simplifying Assumptions -- 2.3.1.1 Deterministic Assumptions -- 2.3.1.2 Stochastic Assumptions -- 2.3.2 The Deterministic Model -- 2.3.3 The Stochastic Model -- 2.4 MODEL PARAMETERIZATION |
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2.4.1 Dividing the Data Set -- 2.4.2 Maximum Likelihood (ML) Method -- 2.4.3 Nonlinear Least Squares (LS) Method -- 2.4.4 Downhill Minimization Routine: Nelder-Mead Algorithm -- 2.4.5 Implementing Parameterization in Code -- 2.4.6 Results of Parameterization -- 2.5 MODEL SELECTION -- 2.6 MODEL VALIDATION -- 2.7 EXERCISES -- BIBLIOGRAPHY -- SECTION II: Discrete-Time Models -- CHAPTER 3 Discrete-Time Maps -- 3.1 WHAT YOU SHOULD KNOW ABOUT THIS CHAPTER -- 3.2 COMPARTMENTAL MODELS -- 3.3 LINEAR MAPS -- 3.3.1 Malthusian Growth -- 3.4 NONLINEAR MAPS -- 3.5 LINEARIZATION |
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3.5.1 Linearization of Functions -- 3.5.2 Linearization of Discrete-Time Maps -- 3.5.3 Linearizing the Ricker Map -- 3.6 THE RICKER NONLINEARITY -- 3.7 EXERCISES -- BIBLIOGRAPHY -- CHAPTER 4 Chaos: Simple Rules Can Generate Complex Results -- 4.1 WHAT YOU SHOULD KNOW ABOUT THIS CHAPTER -- 4.2 RICKER MODEL REVISITED -- 4.3 NEW PARADIGMS ARISE FROM CHAOS -- 4.3.1 Deterministic Unpredictability -- 4.3.2 Complex Results Can Arise from Simple Rules -- 4.4 MAY'S HYPOTHESIS -- 4.5 EXERCISES -- BIBLIOGRAPHY -- CHAPTER 5 Higher-Dimensional Discrete-Time Models |
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5.1 WHAT YOU SHOULD KNOW ABOUT THIS CHAPTER -- 5.2 INTRASPECIFIC INTERACTIONS -- 5.3 INTERSPECIFIC INTERACTIONS -- 5.4 EXAMPLE OF AN AGE-STRUCTURED SINGLE-SPECIES MODEL -- 5.5 EXAMPLE OF A TWO-SPECIES MODEL -- 5.6 n-DIMENSIONAL LINEAR DIFFERENCE EQUATIONS -- 5.6.1 n-Dimensional Leslie Models -- 5.7 SOLVING LINEAR SYSTEMS OF DIFFERENCE EQUATIONS -- 5.7.1 An Example -- 5.7.2 Solving the General Two-Dimensional System -- 5.7.3 Solving Higher-Dimensional Systems -- 5.8 NONLINEAR SYSTEMS -- 5.8.1 Linearization -- 5.8.2 An Example -- 5.9 EXERCISES -- BIBLIOGRAPHY |
| Notes |
Description based upon print version of record |
|
CHAPTER 6 Flour Beetle Dynamics: A Case Study |
| Form |
Electronic book
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| Author |
Hayward, James L
|
| ISBN |
9781000806090 |
|
100080609X |
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