An Analysis of the Catastrophe Model and Catastrophe Characteristics of Traffic Flow Based on Cusp Catastrophe Theory

<div><svg height="8.99888pt" id="M89" style="vertical-align:-3.18151pt" version="1.1" viewbox="-0.0498162 -5.81737 9.68881 8.99888" width="9.68881pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M483 442H303V410C358 401 362 388 351 355C329 286 296 195 278 149C262 190 226 288 200 358C188 393 193 400 239 410V442H-8V410C40 400 53 388 71 344C120 229 165 113 215 -11H254C315 141 364 261 400 342C421 389 433 400 483 410V442Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.045,3.132)"><path d="M52 442L22 406L27 394H92V108C92 45 88 39 30 32V0H302V32C227 39 220 45 220 108V394H321C335 401 339 431 335 442H220L218 477C214 562 214 597 220 616C224 631 233 642 251 642C279 642 311 617 335 593C345 583 355 583 369 593C384 605 395 618 399 629C406 644 405 659 391 673C374 689 349 701 309 703C261 697 226 679 190 649C133 601 112 553 105 531C97 507 92 486 92 464V442H52Z"></path></g></svg>  = 80, the relationship between critical velocity <svg height="9.09935pt" id="M90" style="vertical-align:-3.28198pt" version="1.1" viewbox="-0.0498162 -5.81737 16.7586 9.09935" width="16.7586pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M483 442H303V410C358 401 362 388 351 355C329 286 296 195 278 149C262 190 226 288 200 358C188 393 193 400 239 410V442H-8V410C40 400 53 388 71 344C120 229 165 113 215 -11H254C315 141 364 261 400 342C421 389 433 400 483 410V442Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.045,3.132)"><path d="M699 442H515V410C577 401 582 389 573 351C563 308 532 208 517 161H515C476 254 437 345 401 437H362C326 342 293 250 258 163H256C237 225 217 294 197 358C186 392 192 401 250 410V442H3V410C45 405 55 395 71 347C108 235 151 112 191 -11H229C267 84 302 175 340 268C377 177 418 83 457 -11H495C545 129 587 249 623 342C644 394 651 402 699 410V442Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,12.284,3.132)"><path d="M399 120C363 89 334 79 292 79S154 123 154 256C154 363 199 401 238 401C266 401 298 385 339 349C348 341 354 338 361 338C378 338 404 364 404 393C405 407 401 419 386 429C369 443 336 454 300 454H299C261 454 196 440 130 392C67 345 29 274 29 201C29 92 109 -12 246 -12C307 -12 372 31 418 96L399 120Z"></path></g></svg> with flow <svg height="8.97276pt" id="M91" style="vertical-align:-3.05101pt" version="1.1" viewbox="-0.0498162 -5.92175 7.09377 8.97276" width="7.09377pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M534 -230V-198C472 -191 467 -186 467 -127V336C467 404 469 422 470 442L465 446C441 437 423 434 414 434C403 434 396 435 381 440C370 444 350 451 309 454C158 455 29 343 29 201C29 103 99 -12 259 -12L339 22V-126C339 -187 330 -190 260 -198V-230H534ZM339 58C327 52 317 50 303 50C247 50 170 115 170 235C170 358 226 413 271 413C293 413 319 398 339 372V58Z"></path></g></svg> under different block densities.</div>

Journal of Advanced Transportation

fig9

Figure 9

Figure 9: An Analysis of the Catastrophe Model and Catastrophe Characteristics of Traffic Flow Based on Cusp Catastrophe Theory 