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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 | |