Introduction to the Modeling and Analysis of Complex Systems

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13.3. VISUALIZING TWO-DIMENSIONAL SCALAR AND VECTOR FIELDS 2371.00.50.00.56420246 6402241.06Figure 13.6: Scalar field visualized as a 3-D surface using Code 13.1.
238 CHAPTER 13. CONTINUOUS FIELD MODELS I: MODELINGAnd here is how to draw a contour plot of the same scalar field:Code 13.2: plot-contour.pyfrom pylab import *xvalues, yvalues = meshgrid(arange(-5, 5.5, 0.05), arange(-5, 5.5, 0.05))zvalues = sin(sqrt(xvalues**2 + yvalues**2))cp = contour(xvalues, yvalues, zvalues)clabel(cp)show()The clabel command is used here to add labels to the contours. The result is shown inFig. 13.7.40.2500.000-0.250-0.5000.000-0.5000.5000.2502-0.7500.250-0.250-0.25000.5000.7502-0.5004-0.2500.000-0.7500.0000.5000.750-0.500-0.7504 2 0 2 4-0.2500.000-0.5000.250Figure 13.7: Scalar field visualized as a contour plot using Code 13.2.If you want more color, you can use imshow, which we already used for CA:Code 13.3: plot-imshow.py
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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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Chapter 6Continuous-Time Models I:
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6.2. CLASSIFICATIONS OF MODEL EQUAT
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6.3. CONNECTING CONTINUOUS-TIME MOD
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6.4. SIMULATING CONTINUOUS-TIME MOD
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6.4. SIMULATING CONTINUOUS-TIME MOD
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6.5. BUILDING YOUR OWN MODEL EQUATI
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112 CHAPTER 7. CONTINUOUS-TIME MODE
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Chapter 8Bifurcations8.1 What Are B
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8.2. BIFURCATIONS IN 1-D CONTINUOUS
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8.3. HOPF BIFURCATIONS IN 2-D CONTI
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8.3. HOPF BIFURCATIONS IN 2-D CONTI
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8.4. BIFURCATIONS IN DISCRETE-TIME
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Chapter 9Chaos9.1 Chaos in Discrete
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9.1. CHAOS IN DISCRETE-TIME MODELS
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Next phase space9.3. LYAPUNOV EXPON
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9.3. LYAPUNOV EXPONENT 159easily co
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9.3. LYAPUNOV EXPONENT 16110Lyapuno
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9.4. CHAOS IN CONTINUOUS-TIME MODEL
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Chapter 10Interactive Simulation of
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10.2. INTERACTIVE SIMULATION WITH P
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10.4. SIMULATION WITHOUT PYCX 181Co
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10.4. SIMULATION WITHOUT PYCX 183re
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Chapter 11Cellular Automata I: Mode
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288 CHAPTER 14. CONTINUOUS FIELD MO
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296 CHAPTER 15. BASICS OF NETWORKSg
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298 CHAPTER 15. BASICS OF NETWORKSi
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300 CHAPTER 15. BASICS OF NETWORKS5
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302 CHAPTER 15. BASICS OF NETWORKSE
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304 CHAPTER 15. BASICS OF NETWORKSC
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306 CHAPTER 15. BASICS OF NETWORKSC
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308 CHAPTER 15. BASICS OF NETWORKSt
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312 CHAPTER 15. BASICS OF NETWORKSs
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314 CHAPTER 15. BASICS OF NETWORKSn
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316 CHAPTER 15. BASICS OF NETWORKSL
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318 CHAPTER 15. BASICS OF NETWORKSJ
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320 CHAPTER 15. BASICS OF NETWORKSF
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322 CHAPTER 15. BASICS OF NETWORKSr
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326 CHAPTER 16. DYNAMICAL NETWORKS
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Chapter 17Dynamical Networks II: An
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17.1. NETWORK SIZE, DENSITY, AND PE
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17.1. NETWORK SIZE, DENSITY, AND PE
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17.2. SHORTEST PATH LENGTH 37717.2
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17.2. SHORTEST PATH LENGTH 379Eccen
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17.3. CENTRALITIES AND CORENESS 381
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17.4. CLUSTERING 387while the numer
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17.5. DEGREE DISTRIBUTION 3891.00.8
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17.5. DEGREE DISTRIBUTION 391er = n
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17.5. DEGREE DISTRIBUTION 393Pk = [
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17.5. DEGREE DISTRIBUTION 395logkda
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17.6. ASSORTATIVITY 397Assortativit
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17.6. ASSORTATIVITY 399>>> nx.degre
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17.7. COMMUNITY STRUCTURE AND MODUL
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17.7. COMMUNITY STRUCTURE AND MODUL
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406CHAPTER 18. DYNAMICAL NETWORKS I
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428 CHAPTER 19. AGENT-BASED MODELSE
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430 CHAPTER 19. AGENT-BASED MODELS
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432 CHAPTER 19. AGENT-BASED MODELST
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434 CHAPTER 19. AGENT-BASED MODELSI
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436 CHAPTER 19. AGENT-BASED MODELSt
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438 CHAPTER 19. AGENT-BASED MODELSF
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440 CHAPTER 19. AGENT-BASED MODELSY
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442 CHAPTER 19. AGENT-BASED MODELS3
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444 CHAPTER 19. AGENT-BASED MODELSn
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450 CHAPTER 19. AGENT-BASED MODELSF
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452 CHAPTER 19. AGENT-BASED MODELSe
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454 CHAPTER 19. AGENT-BASED MODELSf
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458 CHAPTER 19. AGENT-BASED MODELSi
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460 CHAPTER 19. AGENT-BASED MODELSw
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462 CHAPTER 19. AGENT-BASED MODELSi
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464 CHAPTER 19. AGENT-BASED MODELSB
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466 BIBLIOGRAPHY[12] “The Human C
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468 BIBLIOGRAPHY[39] H. Sayama, “
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470 BIBLIOGRAPHY[65] P. Holme and J
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Indexaction potential, 202actor, 29
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INDEX 475equilibrium point, 61, 111
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INDEX 477partial differential equat
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Introduction to the Modeling and Analysis of Complex Systems

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