Cover: Qualitative Modeling of Complex Systems: An Introduction to Loop Analysis and Time Averaging, from Harvard University PressCover: Qualitative Modeling of Complex Systems in E-DITION

Qualitative Modeling of Complex Systems

An Introduction to Loop Analysis and Time Averaging

Available from De Gruyter »

Product Details


$65.00 • £54.95 • €60.00

ISBN 9780674435070

Publication Date: 03/14/1986

259 pages



Harvard University Press has partnered with De Gruyter to make available for sale worldwide virtually all in-copyright HUP books that had become unavailable since their original publication. The 2,800 titles in the “e-ditions” program can be purchased individually as PDF eBooks or as hardcover reprint (“print-on-demand”) editions via the “Available from De Gruyter” link above. They are also available to institutions in ten separate subject-area packages that reflect the entire spectrum of the Press’s catalog. More about the E-ditions Program »

  • 1. Qualitative Models
    • Uses of Models
    • Qualitative versus Quantitative Models
    • Preview of Models
    • Limitations of Models
    • Strategy for Qualitative Model Applications
  • 2. Loop Models: Definition of Terms and Calculation of Model Properties
    • Symbols of Signed Digraphs
    • Notation
    • Paths, Links, and Loops
    • Conjunct and Disjunct Loops
    • Feedback
    • Stability
  • 3. Loop Models: Predicting Change
    • Parameter Change
    • Open Paths and Complementary Subsystems
    • Changes in Equilibrium Abundance
    • Tables of Predictions
    • Links from Equations
  • 4. Qualitative Predictions
    • Equilibrium Levels and Turnover Rates
    • Correlations from Predictions
    • From Model to Predictions
    • Some General Observations
    • Lumping Variables
    • Model Ambiguity
    • Experimental Design and Loop Models
    • Correlation Patterns
  • 5. From Concept to Model
    • Ecological Examples
    • Changes in the Graph Structure
    • From Data to Graph
  • 6. Dynamical Systems and Loop Analysis
    • Equilibrium
    • Stability
    • Self-Effect Terms (Self-Damping)
    • Signed Digraphs, the Characteristic Equation, and Feedback
    • Eigenvectors
    • Discrete Systems
  • 7. Time Averaging
    • Definitions
    • Operations with Time Averaging
    • Finite Intervals
    • Discrete-Time Processes
    • Time Averaging and Loop Analysis
    • Linear Equations
    • Nonlinear Equations
  • Appendix: Some Mathematical Operations and Concepts
  • References
  • Index

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