Introduction to the Modeling and Analysis of Complex Systems

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19.3. AGENT-ENVIRONMENT INTERACTION 445# simulating diffusion and evaporation of cAMPfor x in xrange(w):for y in xrange(w):C, R, L, U, D = env[x,y], env[(x+1)%w,y], env[(x-1)%w,y], \env[x,(y+1)%w], env[x,(y-1)%w]lap = (R + L + U + D - 4 * C)/(Dh**2)nextenv[x,y] = env[x,y] + (- k * C + Dc * lap) * Dtenv, nextenv = nextenv, env# simulating secretion of cAMP by agentsfor ag in agents:env[ag.x, ag.y] += f * Dt# simulating chemotaxis of agentsfor ag in agents:newx, newy = (ag.x + randint(-1, 2)) % w, (ag.y + randint(-1, 2)) % wdiff = (env[newx, newy] - env[ag.x, ag.y]) / 0.1if random() < exp(diff) / (1 + exp(diff)):ag.x, ag.y = newx, newyimport pycxsimulatorpycxsimulator.GUI().start(func=[initialize, observe, update])As you see, the code is getting longer and more complicated than before, which is atypical consequence when you implement an ABM.Figure 19.4 shows a typical simulation result. The tiny blue dots represent individualcells (agents), while the grayscale shades on the background show the cAMP concentration(environment). As time goes by, the slightly more populated areas produce morecAMP, attracting more cells. Eventually, several distinct peaks of agent populations arespontaneously formed, reproducing self-organizing patterns that are similar to what thePDE-based model produced.What is unique about this ABM version of the Keller-Segel model, compared to itsoriginal PDE-based version, is that the simulation result looks more “natural”—the formationof the population peaks are not simultaneous, but they gradually appear one afteranother, and the spatial arrangements of those peaks are not regular. In contrast, inthe PDE-based version, the spots are formed simultaneously at regular intervals (see
446 CHAPTER 19. AGENT-BASED MODELS0002020204040406060608080800 20 40 60 800 20 40 60 800 20 40 60 800002020204040406060608080800 20 40 60 800 20 40 60 800 20 40 60 800002020204040406060608080800 20 40 60 800 20 40 60 800 20 40 60 80Figure 19.4: Visual output of Code 19.13. Time flows from left to right, then from topto bottom.
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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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11.1. DEFINITION OF CELLULAR AUTOMA
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11.1. DEFINITION OF CELLULAR AUTOMA
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11.2. EXAMPLES OF SIMPLE BINARY CEL
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11.3. SIMULATING CELLULAR AUTOMATA
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11.5. EXAMPLES OF BIOLOGICAL CELLUL
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Chapter 12Cellular Automata II: Ana
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12.2. PHASE SPACE VISUALIZATION 211
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12.2. PHASE SPACE VISUALIZATION 213
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12.3. MEAN-FIELD APPROXIMATION 215E
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12.3. MEAN-FIELD APPROXIMATION 217T
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12.4. RENORMALIZATION GROUP ANALYSI
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228 CHAPTER 13. CONTINUOUS FIELD MO
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OutIn232 CHAPTER 13. CONTINUOUS FIE
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296 CHAPTER 15. BASICS OF NETWORKSg
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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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Page 485 and 486: 466 BIBLIOGRAPHY[12] “The Human C
Page 487 and 488: 468 BIBLIOGRAPHY[39] H. Sayama, “
Page 489 and 490: 470 BIBLIOGRAPHY[65] P. Holme and J
Page 492 and 493: Indexaction potential, 202actor, 29
Page 494 and 495: INDEX 475equilibrium point, 61, 111
Page 496 and 497: INDEX 477partial differential equat
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Introduction to the Modeling and Analysis of Complex Systems

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