最 低 价：￥470.90
定 价：￥627.83
作 者：Gerda de Vries 著 著
出 版 社：Oversea Publishing House
出版时间：2006-6-1
I S B N：9780898716122
| Gerda de Vries is Associate Professor in the Department of Mathematical and Statistical Sciences at the University of Alberta, Canada. |
| Preface Ⅰ Theoretical Modeling Tools 1 Introduction 1.1 The Modeling Process 1.2 Probabilities and Rates 1.3 Model Classes 1.4 Exercises for Modeling 2 Discrete-Time Models 2.1 Introduction to Discrete-Time Models 2.2 Scalar Discrete-Time Models 2.2.1 Growth of a Population and the Discrete Logistic Equation 2.2.2 Cobwebbing, Fixed Points, and Linear Stability Analysis 2.2.3 Analysis of the Discrete Logistic Equation 2.2.4 Alternatives to the Discrete Logistic Equation 2.2.5 Models in Population Genetics 2.3 Systems of Discrete-Time Equations 2.3.1 Love Affairs: Introduction 2.3.2 Fixed Points and Linear Stability Analysis for Systems of Discrete-Time Equations 2.3.3 Love Affairs: Model Analysis 2.3.4 Host-Parasitoid Models 2.4 Exercises for Discrete-Time Models 3 Ordinary Differential Equations 3.1 Introduction to ODEs 3.2 Scalar Equations 3.2.1 The Picard-Lindeltf Theorem 3.3 Systems of Equations 3.3.1 Reaction Kinetics 3.3.2 A General Interaction Model for Two Populations 3.3.3 A Basic Epidemic Model 3.3.4 Nondimensionalization 3.4 Qualitative Analysis of 2x2 Systems 3.4.1 Phase-Plane Analysis: Linear Systems 3.4.2 Nonlinear Systems and Linearization 3.4.3 Qualitative Analysis of the General Population Interac-tion Model 3.4.4 Qualitative Analysis of the Epidemic Model 3.5 General Systems of Three or More Equations 3.6 Discrete-Time Models from Continuous-Time Models 3.6.1 Numerical Methods 3.6.2 The Time-One Map 3.7 Elementary Bifurcations 3.7.1 Saddle-Node Bifurcation 3.7.2 Transcritical Bifurcation 3.7.3 Pitchfork Bifurcation 3.7.4 Hopf Bifurcation 3.7.5 The Spruce Budwonn Model 3.8 Further Reading 3.9 Exercises for ODEs 4 Partial Differential Equations 4.1 Partial Derivatives 4.2 An Age-Structured Model 4.2.1 Derivation 4.2.2 Solution 4.3 Reaction-Diffusion Equations 4.3.1 Derivation of Reaction-Diffusion Equations 4.3.2 The Fundamental Solution 4.3.3 Critical Domain Size 4.3.4 Traveling Waves 4.4 Further Reading 4.5 Exercises for PDEs 5 Stochastic Models 5.1 Introduction 5.2 Markov Chains 5.2.1 A Two-Tree Forest Ecosystem 5.2.2 Markov Chain Theory 5.2.3 The Princeton Forest Ecosystem 5.3 Working with Random Variables 5.3.1 Probability Density 5.3.2 Probability Mass 5.3.3 Descriptive Statistics 5.3.4 The Generating Function 5.4 Diffusion Processes …… 6 Cellular Automata and Related Models 7 Estimating Parameters Ⅱ Self-Giuided Computer Tutorial 8 Maple Course Ⅲ Projects 9 Project Descriptions 10 Sloved Projects Appendix:Further Reading Bibliography Author Index Index |
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