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| List of Figures | |
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| List of Tables | |
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| Preface | |
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| What Are Dynamic Models? | |
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| Descriptive versus Mechanistic Models | |
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| Chinook Salmon | |
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| Bathtub Models | |
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| Many Bathtubs: Compartment Models | |
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| Enzyme Kinetics | |
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| The Modeling Process | |
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| Pharmacokinetic Models | |
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| Physics Models: Running and Hopping | |
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| Optimization Models | |
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| Why Bother? | |
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| Theoretical versus Practical Models | |
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| What's Next? | |
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| References | |
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| Matrix Models and Structured Population Dynamics | |
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| The Leslie Matrix | |
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| Warning: Prebreeding versus Postbreeding Models | |
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| Matrix Models Based on Stage Classes | |
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| Matrices and Matrix Operations | |
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| Review of Matrix Operations | |
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| Solution of the Matrix Model | |
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| Eigenvalues and a Second Solution of the Model | |
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| Left Eigenvectors | |
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| Some Applications of Matrix Models | |
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| Why Do We Age? | |
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| Elasticity Analysis and Conservation Biology | |
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| How Much Should We Trust These Models? | |
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| Generalizing the Matrix Model | |
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| Stochastic Matrix Models | |
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| Density-Dependent Matrix Models | |
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| Continuous Size Distributions | |
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| Summary and Conclusions | |
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| Appendix | |
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| Existence and Number of Eigenvalues | |
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| Reproductive Value | |
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| References | |
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| Membrane Channels and Action Potentials | |
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| Membrane Currents | |
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| Channel Gating and Conformational States | |
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| Markov Chains | |
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| Coin Tossing | |
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| Markov Chains | |
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| The Neuromuscular Junction | |
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| Voltage-Gated Channels | |
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| Membranes as Electrical Circuits | |
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| Reversal Potential | |
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| Action Potentials | |
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| Summary | |
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| Appendix: The Central Limit Theorem | |
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| References | |
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| Cellular Dynamics: Pathways of Gene Expression | |
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| Biological Background | |
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| A Gene Network That Acts as a Clock | |
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| Formulating a Model | |
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| Model Predictions | |
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| Networks That Act as a Switch | |
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| Systems Biology 125 | |
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| Complex versus Simple Models | |
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| Summary | |
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| References | |
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| Dynamical Systems | |
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| Geometry of a Single Differential Equation | |
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| Mathematical Foundations: A Fundamental Theorem | |
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| Linearization and Linear Systems | |
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| Equilibrium Points | |
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| Linearization at Equilibria | |
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| Solving Linear Systems of Differential Equations | |
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| Invariant Manifolds | |
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| Periodic Orbits | |
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| Phase Planes | |
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| An Example: The Morris-Lecar Model | |
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| Bifurcations | |
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| Numerical Methods | |
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| Summary | |
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| References | |
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| Differential Equation Models for Infectious Disease | |
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| Sir Ronald Ross and the Epidemic Curve | |
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| Rescaling the Model | |
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| Endemic Diseases and Oscillations | |
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| Analysis of the SIR Model with Births | |
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| Summing Up | |
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| Gonorrhea Dynamics and Control | |
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| A Simple Model and a Paradox | |
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| The Core Group | |
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| Implications for Control | |
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| Drug Resistance | |
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| Within-Host Dynamics of HIV | |
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| Conclusions | |
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| References | |
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| Spatial Patterns in Biology | |
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| Reaction-Diffusion Models | |
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| The Turing Mechanism | |
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| Pattern Selection: Steady Patterns | |
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| Moving Patterns: Chemical Waves and Heartbeats | |
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| References | |
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| Agent-Based and Other Computational Models for Complex Systems | |
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| Individual-Based Models in Ecology | |
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| Size-Dependent Predation | |
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| Swarm | |
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| Individual-Based Modeling of Extinction Risk | |
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| Artificial Life | |
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| Tierr | |