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| Preface to the Classics Edition | |
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| Preface | |
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| Acknowledgments | |
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| Errata | |
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| Discrete Process in Biology | |
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| The Theory of Linear Difference Equations Applied to Population Growth | |
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| Biological Models Using Difference Equations | |
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| Cell Division | |
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| An Insect Population | |
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| Propagation of Annual Plants | |
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| Statement of the Problem | |
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| Definitions and Assumptions | |
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| The Equations | |
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| Condensing the Equations | |
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| Check | |
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| Systems of Linear Difference Equations | |
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| A Linear Algebra Review | |
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| Will Plants Be Successful? | |
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| Qualitative Behavior of Solutions to Linear Difference Equations | |
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| The Golden Mean Revisited | |
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| Complex Eigenvalues in Solutions to Difference Equations | |
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| Related Applications to Similar Problems | |
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| Growth of Segmental Organisms | |
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| A Schematic Model of Red Blood Cell Production | |
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| Ventilation Volume and Blood CO[subscript 2] Levels | |
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| For Further Study: Linear Difference Equations in Demography | |
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| Problems | |
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| References | |
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| Nonlinear Difference Equations | |
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| Recognizing a Nonlinear Difference Equation | |
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| Steady States, Stability, and Critical Parameters | |
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| The Logistic Difference Equation | |
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| Beyond r = 3 | |
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| Graphical Methods for First-Order Equations | |
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| A Word about the Computer | |
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| Systems of Nonlinear Difference Equations | |
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| Stability Criteria for Second-Order Equations | |
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| Stability Criteria for Higher-Order Systems | |
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| For Further Study: Physiological Applications | |
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| Problems | |
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| References | |
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| Appendix to Chapter 2: Taylor Series | |
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| Functions of One Variable | |
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| Functions of Two Variables | |
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| Applications of Nonlinear Difference Equations to Population Biology | |
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| Density Dependence in Single-Species Populations | |
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| Two-Species Interactions: Host-Parasitoid Systems | |
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| The Nicholson-Bailey Model | |
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| Modifications of the Nicholson-Bailey Model | |
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| Density Dependence in the Host Population | |
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| Other Stabilizing Factors | |
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| A Model for Plant-Herbivore Interactions | |
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| Outlining the Problem | |
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| Rescaling the Equations | |
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| Further Assumptions and Stability Calculations | |
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| Deciphering the Conditions for Stability | |
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| Comments and Extensions | |
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| For Further Study: Population Genetics | |
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| Problems | |
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| Projects | |
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| References | |
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| Continuous Processes and Ordinary Differential Equations | |
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| An Introduction to Continuous Models | |
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| Warmup Examples: Growth of Microorganisms | |
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| Bacterial Growth in a Chemostat | |
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| Formulating a Model | |
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| First Attempt | |
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| Corrected Version | |
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| A Saturating Nutrient Consumption Rate | |
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| Dimensional Analysis of the Equations | |
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| Steady-State Solutions | |
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| Stability and Linearization | |
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| Linear Ordinary Differential Equations: A Brief Review | |
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| First-Order ODEs | |
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| Second-Order ODEs | |
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| A System of Two First-Order Equations (Elimination Method) | |
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| A System of Two First-Order Equations (Eigenvalue-Eigenvector Method) | |
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| When Is a Steady State Stable? | |
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| Stability of Steady States in the Chemostat | |
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| Applications to Related Problems | |
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| Delivery of Drugs by Continuous Infusion | |
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| Modeling of Glucose-Insulin Kinetics | |
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| Compartmental Analysis | |
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| Problems | |
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| References | |
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| Phase-Plane Methods and Qualitative Solutions | |
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| First-Order ODEs: A Geometric Meaning | |
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| Systems of Two First-Order ODEs | |
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| Curves in the Plane | |
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| The Direction Field | |
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| Nullclines: A More Systematic Approach | |
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| Close to the Steady States | |
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| Phase-Plane Diagrams of Linear Systems | |
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| Real Eigenvalues | |
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| Complex Eigenvalues | |
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| Classifying Stability Characteristics | |
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| Global Behavior from Local Information | |
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| Constructing a Phase-Plane Diagram for the Chemostat | |
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| The Nullclines | |
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| Steady States | |
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| Close to Steady States | |
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| Interpreting the Solutions | |
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| Higher-Order Equations | |
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| Problems | |
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| References | |
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| Applications of Continuous Models to Population Dynamics | |
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| Models for Single-Species Populations | |
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| Malthus Model | |
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| Logistic Growth | |
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| Allee Effect | |
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| Other Assumptions; Gompertz Growth in Tumors | |
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| Predator-Prey Systems and the Lotka-Volterra Equations | |
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| Populations in Competition | |
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| Multiple-Species Communities and the Routh-Hurwitz Criteria | |
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| Qualitative Stability | |
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| The Population Biology of Infectious Diseases | |
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| For Further Study: Vaccination Policies | |
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| Eradicating a Disease | |
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| Average Age of Acquiring a Disease | |
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| Models for Molecular Events | |
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| Michaelis-Menten Kinetics | |
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| The Quasi-Steady-State Assumption | |
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| A Quick, Easy Derivation of Sigmoidal Kinetics | |
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| Cooperative Reactions and the Sigmoidal Response | |
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| A Molecular Model for Threshold-Governed Cellular Development | |
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| Species Competition in a Chemical Setting | |
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| A Bimolecular Switch | |
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| Stability of Activator-Inhibitor and Positive Feedback Systems | |
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| The Activator-Inhibitor System | |
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| Positive Feedback | |
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| Some Extensions and Suggestions for Further Study | |
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| Limit Cycles, Oscillations, and Excitable Systems | |
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| Nerve Conduction, the Action Potential, and the Hodgkin-Huxley Equations | |
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| Fitzhugh's Analysis of the Hodgkin-Huxley Equations | |
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| The Poincare-Bendixson Theory | |
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| The Case of the Cubic Nullclines | |
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| The Fitzhugh-Nagumo Model for Neural Impulses | |
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| The Hopf Bifurcation | |
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| Oscillations in Population-Based Models | |
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| Oscillations in Chemical Systems | |
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| Criteria for Oscillations in a Chemical System | |
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| For Further Study: Physiological and Circadian Rhythms | |
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| Appendix to Chapter 8. Some Basic Topological Notions | |
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| Appendix to Chapter 8. More about the Poincare-Bendixson Theory | |
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| Spatially Distributed Systems and Partial Differential Equation Models | |
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| An Introduction to Partial Differential Equations and Diffusion in Biological Settings | |
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| Functions of Several Variables: A Review | |
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| A Quick Derivation of the Conservation Equation | |
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| Other Versions of the Conservation Equation | |
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| Tubular Flow | |
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| Flows in Two and Three Dimensions | |
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| Convection, Diffusion, and Attraction | |
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| Convection | |
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| Attraction or Repulsion | |
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| Random Motion and the Diffusion Equation | |
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| The Diffusion Equation and Some of Its Consequences | |
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| Transit Times for Diffusion | |
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| Can Macrophages Find Bacteria by Random Motion Alone? | |
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| Other Observations about the Diffusion Equation | |
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| An Application of Diffusion to Mutagen Bioassays | |
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| Appendix to Chapter 9. Solutions to the One-Dimensional Diffusion Equation | |
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| Partial Differential Equation Models in Biology | |
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| Population Dispersal Models Based on Diffusion | |
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| Random and Chemotactic Motion of Microorganisms | |
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| Density-Dependent Dispersal | |
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| Apical Growth in Branching Networks | |
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| Simple Solutions: Steady States and Traveling Waves | |
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| Nonuniform Steady States | |
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| Homogeneous (Spatially Uniform) Steady States | |
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| Traveling-Wave Solutions | |
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| Traveling Waves in Microorganisms and in the Spread of Genes | |
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| Fisher's Equation: The Spread of Genes in a Population | |
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| Spreading Colonies of Microorganisms | |
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| Some Perspectives and Comments | |
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| Transport of Biological Substances Inside the Axon | |
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| Conservation Laws in Other Settings: Age Distributions and the Cell Cycle | |
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| The Cell Cycle | |
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| Analogies with Particle Motion | |
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| A Topic for Further Study: Applications to Chemotherapy | |
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| Summary | |
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| A Do-It-Yourself Model of Tissue Culture | |
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| A Statement of the Biological Problem | |
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| A Simple Case | |
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| A Slightly More Realistic Case | |
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| Writing the Equations | |
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| The Final Step | |
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| Discussion | |
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| For Further Study: Other Examples of Conservation Laws in Biological Systems | |
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| Models for Development and Pattern Formation in Biological Systems | |
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| Cellular Slime Molds | |
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| Homogeneous Steady States and Inhomogeneous Perturbations | |
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| Interpreting the Aggregation Condition | |
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| A Chemical Basis for Morphogenesis | |
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| Conditions for Diffusive Instability | |
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| A Physical Explanation | |
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| Extension to Higher Dimensions and Finite Domains | |
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| Applications to Morphogenesis | |
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| For Further Study | |
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| Patterns in Ecology | |
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| Evidence for Chemical Morphogens in Developmental Systems | |
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| A Broader View of Pattern Formation in Biology | |
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| Selected Answers | |
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| Author Index | |
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| Subject Index | |