Graph Algebra: Mathematical Modeling with a Systems Approach (Quantitative Applications in the Social Sciences v. 151)
By: Courtney M. Brown (author)Paperback
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Derived from engineering literature that uses similar techniques to map electronic circuits and physical systems, graph algebra utilizes a systems approach to modelling that offers social scientists a variety of tools that are both sophisticated and easily applied.
Courtney Brown is an Associate Professor in the Department of Political Science at Emory University. Dr. Brown has taught differential equation modeling to graduate and undergraduate students for over 20 years. His teaching and research interests also include other quantitative methods, political musicology, science fiction and politics, electoral behavior, political parties, democratic development, and politics and the environment. He has authored five books that deal with differential equation models in the social sciences, including three titles for the Quantitative Applications in the Social Sciences series.
Series Editor's Introduction Acknowledgments 1. Systems Analysis Structure and Function An Overview of the Substantive Examples Found in Subsequent Chapters 2. Graph Algebra Basics Inputs, Outputs, and the Forward Path Feedback Loops and Mason's Rule An Example From Economics: The Keynesian Multiplier 3. Graph Algebra and Discrete-Time Linear Operators Delay and Advance Operators for Discrete Time Including an Additive Constant With Graph Algebra Difference and Summation Operators for Discrete Time An Estimated Example: Labor Union Membership 4. Working With Systems of Equations Richardson's Arms Race Model Using Graph Algebra Variations of Richardson's Arms Race Model An Estimated Example of a Multiple-Equation System With Nonlinear or Embedded Parameters: Richardson's Arms Race 5. Applying Graph Algebra to Continuous Time Using Graph Algebra With Continuous-Time Operators 6. Graph Algebra and Nonlinearity Nonlinear Filters The Logistic Function Placement Rules for Operators in Nonlinear Models Graph Algebra and Chaos Forced Oscillators 7. Working With Conditional Paths Logical and Decision Systems An Example of Democratic Transition 8. Systems, Shocks, and Stochasticity 9. Graph Algebra and Social Theory Systems and Equilibria References Index About the Author
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