Introduction to the Modeling and Analysis of Complex Systems

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5.7. LINEAR STABILITY ANALYSIS OF DISCRETE-TIME NONLINEAR... 971. Find all equilibrium points (which you may have done already in Exercise 5.2).2. Calculate the Jacobian matrix at each of the equilibrium points.3. Calculate the eigenvalues of each of the matrices obtained above.4. Based on the results, discuss the stability of each equilibrium point.
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Introduction to the Modeling and An
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iiiAbout the TextbookIntroduction t
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New York. He is also a Fellow of th
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PrefaceThis is an introductory text
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a comprehensive view of the related
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Chen, Hal Lewis, Vlad Miskovic, Chu
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xviCONTENTS5 Discrete-Time Models I
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xviiiCONTENTS15.3 Constructing Netw
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Chapter 1Introduction1.1 Complex Sy
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1.1. COMPLEX SYSTEMS IN A NUTSHELL
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1.2. TOPICAL CLUSTERS 7The possibil
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1.2. TOPICAL CLUSTERS 9these topica
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12 CHAPTER 2. FUNDAMENTALS OF MODEL
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Part IISystems with a Small Number
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30 CHAPTER 3. BASICS OF DYNAMICAL S
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36 CHAPTER 4. DISCRETE-TIME MODELS
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Page 132 and 133: 7.2. PHASE SPACE VISUALIZATION 113s
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148 CHAPTER 8. BIFURCATIONS2.0r = 0
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150 CHAPTER 8. BIFURCATIONSdef init
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152 CHAPTER 8. BIFURCATIONSExercise
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154 CHAPTER 9. CHAOS2.52.01.51.00.5
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156 CHAPTER 9. CHAOS0.8Logistic map
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158 CHAPTER 9. CHAOS1.00.80.60.40.2
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160 CHAPTER 9. CHAOSreturn log(abs(
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162 CHAPTER 9. CHAOSThen explain in
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164 CHAPTER 9. CHAOSfigure()ax = gc
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166 CHAPTER 9. CHAOS20 15 10 05 051
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168 CHAPTER 9. CHAOScan’t cross,
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Part IIISystems with a Large Number
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174 CHAPTER 10. INTERACTIVE SIMULAT
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186 CHAPTER 11. CELLULAR AUTOMATA I
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Chapter 13Continuous Field Models I
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13.2. FUNDAMENTALS OF VECTOR CALCUL
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13.3. VISUALIZING TWO-DIMENSIONAL S
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13.3. VISUALIZING TWO-DIMENSIONAL S
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13.4. MODELING SPATIAL MOVEMENT 241
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13.5. SIMULATION OF CONTINUOUS FIEL
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13.6. REACTION-DIFFUSION SYSTEMS 25
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Chapter 14Continuous Field Models I
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14.1. FINDING EQUILIBRIUM STATES 27
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14.2. VARIABLE RESCALING 273Exercis
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14.3. LINEAR STABILITY ANALYSIS OF
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Chapter 15Basics of Networks15.1 Ne
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15.2. TERMINOLOGIES OF GRAPH THEORY
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15.3. CONSTRUCTING NETWORK MODELS W
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15.4. VISUALIZING NETWORKS WITH NET
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15.4. VISUALIZING NETWORKS WITH NET
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15.5. IMPORTING/EXPORTING NETWORK D
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15.6. GENERATING RANDOM GRAPHS 321s
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15.6. GENERATING RANDOM GRAPHS 323R
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Chapter 16Dynamical Networks I: Mod
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16.2. SIMULATING DYNAMICS ON NETWOR
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16.3. SIMULATING DYNAMICS OF NETWOR
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16.4. SIMULATING ADAPTIVE NETWORKS
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372CHAPTER 17. DYNAMICAL NETWORKS I
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Chapter 18Dynamical Networks III: A
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18.2. DIFFUSION ON NETWORKS 40718.2
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18.3. SYNCHRONIZABILITY 4092.749157
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18.3. SYNCHRONIZABILITY 411The firs
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18.3. SYNCHRONIZABILITY 413nextg =
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18.3. SYNCHRONIZABILITY 415(a)1.0(b
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18.5. MEAN-FIELD APPROXIMATION ON R
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18.5. MEAN-FIELD APPROXIMATION ON R
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18.6. MEAN-FIELD APPROXIMATION ON S
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Chapter 19Agent-Based Models19.1 Wh
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19.1. WHAT ARE AGENT-BASED MODELS?
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19.2. BUILDING AN AGENT-BASED MODEL
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19.3. AGENT-ENVIRONMENT INTERACTION
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19.4. ECOLOGICAL AND EVOLUTIONARY M
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Bibliography[1] H. A. Simon, “The
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BIBLIOGRAPHY 467[26] J. D. Sterman,
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BIBLIOGRAPHY 469[52] J. E. Pearson,
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BIBLIOGRAPHY 471[78] M. E. Newman a
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474 INDEXcomplex adaptive system, 8
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476 INDEXlinear system, 36lineariza
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478 INDEXstate-transition function,
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Introduction to the Modeling and Analysis of Complex Systems

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