Models for Research and Understanding: Exploring Dynamic Systems, Unconventional Approaches, and Applications

Preface
Acknowledgements
Contents
1 Concept of Model
	1.1 Introduction: General Remarks
	1.2 The System
	1.3 Mathematical Models
		1.3.1 Kinds of Mathematical Models
		1.3.2 Models of Economic Growth
		1.3.3 Models in Public Health and Epidemics
		1.3.4 Graphical Representations of Continuous Models
		1.3.5 Computational Tractability
	1.4 Discrete-Event Models
		1.4.1 Petri Nets
		1.4.2 Discrete-Event Specification Formalism (DEVS)
	1.5 Experimental Frames and Model Validity
		1.5.1 Two Capacitors Circuit
		1.5.2 Birth-and-death Process
	1.6 Model Credibility
	1.7 Uncertainty and Randomness
	1.8 Conclusion
	1.9 Questions and Answers
	References
2 Continuous System Models
	2.1 Introduction
	2.2 Dynamic Systems
		2.2.1 General Classification
	2.3 Linearity
	2.4 Ordinary Differential Equations and Models of Systems …
	2.5 Transfer Function
		2.5.1 Stability of Linear Models
		2.5.2 Routh–Hurwitz Stability Criterion
		2.5.3 Frequency Response
	2.6 Nyquist Plot and Stability Criterion
	2.7 Analog Computer Models
	2.8 Z-transform
		2.8.1 Matched Pole-zero
	2.9 Non-linear Models and Stability
		2.9.1 BIBO Stability
		2.9.2 Lyapunov Stability
		2.9.3 Asymptotic Stability
		2.9.4 Orbital Stability
	2.10 Stiff Equations
	2.11 Example: ODE Model of a Car Suspension
	2.12 Graphical Representations of Continuous Models
		2.12.1 Block Diagrams and Signal Flow Graphs
		2.12.2 Mason's Gain Formula
		2.12.3 Bond Graphs
		2.12.4 Example of Bond Graph
		2.12.5 The Causality and DYMOLA
	2.13 Models with Distributed Parameters, Partial Differential Equations
		2.13.1 PDE Solution Algorithms
		2.13.2 Finite Element Model
		2.13.3 Example: Jet Takeoff Vibrations
	2.14 Conclusion
	2.15 Questions and Answers
	References
3 Differential Inclusions, Uncertainty, and Functional Sensitivity
	3.1 Introduction, Some Definitions
	3.2 Differential Inclusions
	3.3 Reachable Set
	3.4 Differential Inclusions and Control Systems
		3.4.1 Uncertainty Treatment
	3.5 Functional Sensitivity
	3.6 Differential Inclusion Solver
		3.6.1 Example: A Second-Order Model
	3.7 Discrete Differential Inclusions
		3.7.1 Reachable Set, Optimal Trajectory
		3.7.2 Example 1
		3.7.3 Example 2
	3.8 Conclusion
	3.9 Questions and Answers
	References
4 Functional Sensitivity Applications
	4.1 Introduction
	4.2 Functional Sensitivity
		4.2.1 Differential Inclusions
		4.2.2 Sensitivity Analysis
	4.3 Differential Inclusion Solver
	4.4 Example: The Lotka–Volterra Model
	4.5 A Mechanical System
	4.6 Functional Sensitivity of the V/f Speed Control  of Induction Motor
		4.6.1 Comparison with the Classical Sensitivity Analysis
	4.7 PID Anti-Windup Control
	4.8 Vehicle Horizontal Movement
	4.9 Marketing Sensibility and Reachable Sets
		4.9.1 The Model
		4.9.2 Experiment 1
		4.9.3 Experiment 2
	4.10 Conclusion
	4.11 Questions and Answers
	References
5 Attainable Sets in Flight Control
	5.1 Introduction
	5.2 Control and Reachable Sets
		5.2.1 Airplane Dynamics
		5.2.2 Attainable Sets
	5.3 Conclusion
	5.4 Questions and Answers
	References
6 Modeling, Simulation, and Optimization
	6.1 Introduction
	6.2 Landing on the Moon
	6.3 Iterative Algorithm
	6.4 Market Optimization
	6.5 Computer Implementation: Simulation and Optimization
	6.6 Conclusion
	6.7 Questions and Answers
	References
7 Discrete Event Models
	7.1 Introduction
	7.2 The Event Queue
	7.3 Agent-Based Models
		7.3.1 People Agents
	7.4 Discrete Event Specification Formalism (DEVS)
		7.4.1 A Remark on Ambiguity
		7.4.2 DEVS
	7.5 Petri Nets
	7.6 Distributed Simulation Models
	7.7 Conclusion
	7.8 Questions and Answers
	References
8 Self-Organization, Organization Dynamics, and Agent-Based Model
	8.1 Introduction
	8.2 The Model
		8.2.1 Interaction Rules
	8.3 BLUESSS Simulation Package
	8.4 Simulations
	8.5 Conclusion
	8.6 Questions and Answers
	References
9 The Space of Models, Semi-Discrete Events with Fuzzy Logic
	9.1 Introduction
		9.1.1 Distance Between Models
	9.2 Strictly Discrete Event Model
	9.3 Finite-Time Event Model
		9.3.1 The Chicken Game
		9.3.2 Semi-Discrete Model Specification
		9.3.3 Model Coupling
	9.4 More Examples
		9.4.1 Example 1: One Server
		9.4.2 Example 2: Two Servers
		9.4.3 Example 3: A Battlefield
	9.5 Singularity of the Exact DES Models
	9.6 Conclusion
	9.7 Questions and Answers
	References
10 Models and Categories
	10.1 Introduction: The Language of Categories
		10.1.1 Examples
		10.1.2 Simultaneous Events
	10.2 Conclusion
	10.3 Questions and Answers
	References
11 Fuzzy Time Instants and Time Model
	11.1 Introduction
	11.2 The Fuzzy Time Instant
		11.2.1 Example
	11.3 Conclusion
	References
12 Uncertain Future, Reversibility and the Fifth Dimension
	12.1 Introduction
	12.2 Uncertain Future
	12.3 Differential Inclusion Solver
	12.4 Solving the Ideal Predictor Problem. Feedback From the Future
		12.4.1 Example 1: A Linear Model
		12.4.2 Example 2: A Non-Linear Model
		12.4.3 Example 3: A Control System
	12.5 Reversibility
		12.5.1 Irreversibility of Differential Inclusions
	12.6 Encapsulated Universe and the Fifth Dimension
		12.6.1 General Remarks
		12.6.2 The Ball
		12.6.3 The Metric Structure
		12.6.4 Linear Vector Space Operators
		12.6.5 Local Ball and Local Observer
		12.6.6 Velocity Superposition
		12.6.7 Particle Movement and a Small Bang
		12.6.8 Adding the Time Dimension
		12.6.9 Uncertainty and Traveling Beyond the Infinity
		12.6.10 The Fifth Dimension
		12.6.11 Conclusion
	References
Appendix  Index
Index