Introduction to the Modeling and Analysis of Complex Systems

Recommendations

Info

13.3. VISUALIZING TWO-DIMENSIONAL SCALAR AND VECTOR FIELDS 239from pylab import *xvalues, yvalues = meshgrid(arange(-5, 5.5, 0.05), arange(-5, 5.5, 0.05))zvalues = sin(sqrt(xvalues**2 + yvalues**2))imshow(zvalues)show()The result is shown in Fig. 13.8. Colorful!0501001502000 50 100 150 200Figure 13.8: Scalar field visualized as a color image using Code 13.3.Finally, a two-dimensional vector field can be visualized using the streamplot functionthat we used in Section 7.2. Here is an example of the visualization of a vector fieldv = (v x , v y ) = (2x, y − x), with the result shown in Fig. 13.9:Code 13.4: plot-vector-field.pyfrom pylab import *
240 CHAPTER 13. CONTINUOUS FIELD MODELS I: MODELINGxvalues, yvalues = meshgrid(arange(-3, 3.1, 0.1), arange(-3, 3.1, 0.1))vx = 2 * xvaluesvy = yvalues - xvaluesstreamplot(xvalues, yvalues, vx, vy)show()32101233 2 1 0 1 2 3Figure 13.9: Vector field visualized using Code 13.4.Exercise 13.7Python.Plot the scalar field f(x, y) = sin(xy) for −4 ≤ x, y ≤ 4 usingExercise 13.8Python.Plot the gradient field of f(x, y) = sin(xy) for −4 ≤ x, y ≤ 4 using
Page 2 and 3:
Introduction to the Modeling and An
Page 4 and 5:
iiiAbout the TextbookIntroduction t
Page 6:
New York. He is also a Fellow of th
Page 10 and 11:
PrefaceThis is an introductory text
Page 12 and 13:
a comprehensive view of the related
Page 14:
Chen, Hal Lewis, Vlad Miskovic, Chu
Page 17 and 18:
xviCONTENTS5 Discrete-Time Models I
Page 19 and 20:
xviiiCONTENTS15.3 Constructing Netw
Page 22 and 23:
Chapter 1Introduction1.1 Complex Sy
Page 24 and 25:
1.1. COMPLEX SYSTEMS IN A NUTSHELL
Page 26 and 27:
1.2. TOPICAL CLUSTERS 7The possibil
Page 28:
1.2. TOPICAL CLUSTERS 9these topica
Page 31 and 32:
12 CHAPTER 2. FUNDAMENTALS OF MODEL
Page 33 and 34:
Page 35 and 36:
Page 37 and 38:
Page 39 and 40:
Page 41 and 42:
Page 43 and 44:
Page 46:
Part IISystems with a Small Number
Page 49 and 50:
30 CHAPTER 3. BASICS OF DYNAMICAL S
Page 51 and 52:
Page 53 and 54:
Page 55 and 56:
36 CHAPTER 4. DISCRETE-TIME MODELS
Page 57 and 58:
Page 59 and 60:
Page 61 and 62:
Page 63 and 64:
Page 65 and 66:
Page 67 and 68:
Page 69 and 70:
Page 71 and 72:
Page 73 and 74:
Page 75 and 76:
Page 77 and 78:
Page 79 and 80:
Page 81 and 82:
Page 83 and 84:
Page 85 and 86:
Page 87 and 88:
Page 89 and 90:
Page 91 and 92:
Page 93 and 94:
Page 95 and 96:
Page 97 and 98:
Page 99 and 100:
Page 101 and 102:
Page 103 and 104:
Page 105 and 106:
Page 107 and 108:
Page 109 and 110:
Page 111 and 112:
Page 113 and 114:
Page 115 and 116:
Page 118 and 119:
Chapter 6Continuous-Time Models I:
Page 120 and 121:
6.2. CLASSIFICATIONS OF MODEL EQUAT
Page 122 and 123:
6.3. CONNECTING CONTINUOUS-TIME MOD
Page 124 and 125:
6.4. SIMULATING CONTINUOUS-TIME MOD
Page 126 and 127:
6.4. SIMULATING CONTINUOUS-TIME MOD
Page 128:
6.5. BUILDING YOUR OWN MODEL EQUATI
Page 131 and 132:
112 CHAPTER 7. CONTINUOUS-TIME MODE
Page 133 and 134:
Page 135 and 136:
Page 137 and 138:
Page 139 and 140:
Page 141 and 142:
Page 143 and 144:
Page 145 and 146:
Page 147 and 148:
Page 150 and 151:
Chapter 8Bifurcations8.1 What Are B
Page 152 and 153:
8.2. BIFURCATIONS IN 1-D CONTINUOUS
Page 154 and 155:
Page 156 and 157:
Page 158 and 159:
Page 160 and 161:
8.3. HOPF BIFURCATIONS IN 2-D CONTI
Page 162 and 163:
8.3. HOPF BIFURCATIONS IN 2-D CONTI
Page 164 and 165:
8.4. BIFURCATIONS IN DISCRETE-TIME
Page 166 and 167:
Page 168 and 169:
Page 170 and 171:
Page 172 and 173:
Chapter 9Chaos9.1 Chaos in Discrete
Page 174 and 175:
9.1. CHAOS IN DISCRETE-TIME MODELS
Page 176 and 177:
Next phase space9.3. LYAPUNOV EXPON
Page 178 and 179:
9.3. LYAPUNOV EXPONENT 159easily co
Page 180 and 181:
9.3. LYAPUNOV EXPONENT 16110Lyapuno
Page 182 and 183:
9.4. CHAOS IN CONTINUOUS-TIME MODEL
Page 184 and 185:
Page 186 and 187:
Page 188:
Page 192 and 193:
Chapter 10Interactive Simulation of
Page 194 and 195:
10.2. INTERACTIVE SIMULATION WITH P
Page 196 and 197:
Page 198 and 199:
Page 200 and 201:
10.4. SIMULATION WITHOUT PYCX 181Co
Page 202 and 203:
10.4. SIMULATION WITHOUT PYCX 183re
Page 204 and 205:
Chapter 11Cellular Automata I: Mode
Page 206 and 207:
11.1. DEFINITION OF CELLULAR AUTOMA
Page 208 and 209: 11.1. DEFINITION OF CELLULAR AUTOMA
Page 210 and 211: 11.2. EXAMPLES OF SIMPLE BINARY CEL
Page 212 and 213: 11.3. SIMULATING CELLULAR AUTOMATA
Page 220 and 221: 11.5. EXAMPLES OF BIOLOGICAL CELLUL
Page 228 and 229: Chapter 12Cellular Automata II: Ana
Page 230 and 231: 12.2. PHASE SPACE VISUALIZATION 211
Page 232 and 233: 12.2. PHASE SPACE VISUALIZATION 213
Page 234 and 235: 12.3. MEAN-FIELD APPROXIMATION 215E
Page 236 and 237: 12.3. MEAN-FIELD APPROXIMATION 217T
Page 238 and 239: 12.4. RENORMALIZATION GROUP ANALYSI
Page 244: 12.4. RENORMALIZATION GROUP ANALYSI
Page 247 and 248: 228 CHAPTER 13. CONTINUOUS FIELD MO
Page 251 and 252: OutIn232 CHAPTER 13. CONTINUOUS FIE
Page 257: 238 CHAPTER 13. CONTINUOUS FIELD MO
Page 309 and 310:
290 CHAPTER 14. CONTINUOUS FIELD MO
Page 311 and 312:
Page 313 and 314:
Page 315 and 316:
296 CHAPTER 15. BASICS OF NETWORKSg
Page 317 and 318:
298 CHAPTER 15. BASICS OF NETWORKSi
Page 319 and 320:
300 CHAPTER 15. BASICS OF NETWORKS5
Page 321 and 322:
302 CHAPTER 15. BASICS OF NETWORKSE
Page 323 and 324:
304 CHAPTER 15. BASICS OF NETWORKSC
Page 325 and 326:
306 CHAPTER 15. BASICS OF NETWORKSC
Page 327 and 328:
308 CHAPTER 15. BASICS OF NETWORKSt
Page 329 and 330:
Page 331 and 332:
312 CHAPTER 15. BASICS OF NETWORKSs
Page 333 and 334:
314 CHAPTER 15. BASICS OF NETWORKSn
Page 335 and 336:
316 CHAPTER 15. BASICS OF NETWORKSL
Page 337 and 338:
318 CHAPTER 15. BASICS OF NETWORKSJ
Page 339 and 340:
320 CHAPTER 15. BASICS OF NETWORKSF
Page 341 and 342:
322 CHAPTER 15. BASICS OF NETWORKSr
Page 343 and 344:
Page 345 and 346:
326 CHAPTER 16. DYNAMICAL NETWORKS
Page 347 and 348:
Page 349 and 350:
Page 351 and 352:
Page 353 and 354:
Page 355 and 356:
Page 357 and 358:
Page 359 and 360:
Page 361 and 362:
Page 363 and 364:
Page 365 and 366:
Page 367 and 368:
Page 369 and 370:
Page 371 and 372:
Page 373 and 374:
Page 375 and 376:
Page 377 and 378:
Page 379 and 380:
Page 381 and 382:
Page 383 and 384:
Page 385 and 386:
Page 387 and 388:
Page 390 and 391:
Chapter 17Dynamical Networks II: An
Page 392 and 393:
17.1. NETWORK SIZE, DENSITY, AND PE
Page 394 and 395:
17.1. NETWORK SIZE, DENSITY, AND PE
Page 396 and 397:
17.2. SHORTEST PATH LENGTH 37717.2
Page 398 and 399:
17.2. SHORTEST PATH LENGTH 379Eccen
Page 400 and 401:
17.3. CENTRALITIES AND CORENESS 381
Page 402 and 403:
Page 404 and 405:
Page 406 and 407:
17.4. CLUSTERING 387while the numer
Page 408 and 409:
17.5. DEGREE DISTRIBUTION 3891.00.8
Page 410 and 411:
17.5. DEGREE DISTRIBUTION 391er = n
Page 412 and 413:
17.5. DEGREE DISTRIBUTION 393Pk = [
Page 414 and 415:
17.5. DEGREE DISTRIBUTION 395logkda
Page 416 and 417:
17.6. ASSORTATIVITY 397Assortativit
Page 418 and 419:
17.6. ASSORTATIVITY 399>>> nx.degre
Page 420 and 421:
17.7. COMMUNITY STRUCTURE AND MODUL
Page 422:
17.7. COMMUNITY STRUCTURE AND MODUL
Page 425 and 426:
406CHAPTER 18. DYNAMICAL NETWORKS I
Page 427 and 428:
Page 429 and 430:
Page 431 and 432:
Page 433 and 434:
Page 435 and 436:
Page 437 and 438:
Page 439 and 440:
Page 441 and 442:
Page 443 and 444:
Page 445 and 446:
Page 447 and 448:
428 CHAPTER 19. AGENT-BASED MODELSE
Page 449 and 450:
430 CHAPTER 19. AGENT-BASED MODELS
Page 451 and 452:
432 CHAPTER 19. AGENT-BASED MODELST
Page 453 and 454:
434 CHAPTER 19. AGENT-BASED MODELSI
Page 455 and 456:
436 CHAPTER 19. AGENT-BASED MODELSt
Page 457 and 458:
438 CHAPTER 19. AGENT-BASED MODELSF
Page 459 and 460:
440 CHAPTER 19. AGENT-BASED MODELSY
Page 461 and 462:
442 CHAPTER 19. AGENT-BASED MODELS3
Page 463 and 464:
444 CHAPTER 19. AGENT-BASED MODELSn
Page 465 and 466:
Page 467 and 468:
Page 469 and 470:
450 CHAPTER 19. AGENT-BASED MODELSF
Page 471 and 472:
452 CHAPTER 19. AGENT-BASED MODELSe
Page 473 and 474:
454 CHAPTER 19. AGENT-BASED MODELSf
Page 475 and 476:
Page 477 and 478:
458 CHAPTER 19. AGENT-BASED MODELSi
Page 479 and 480:
460 CHAPTER 19. AGENT-BASED MODELSw
Page 481 and 482:
462 CHAPTER 19. AGENT-BASED MODELSi
Page 483 and 484:
464 CHAPTER 19. AGENT-BASED MODELSB
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
show all

Introduction to the Modeling and Analysis of Complex Systems

Create successful ePaper yourself

Delete template?

Save as template?