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

<div><svg height="14.6509pt" id="M82" style="vertical-align:-5.41477pt" version="1.1" viewbox="-0.0498162 -9.23613 9.92237 14.6509" width="9.92237pt" 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="M535 0V32C500 38 483 46 451 83C420 121 333 240 306 284C336 322 350 339 377 366C405 394 440 407 502 418V448L286 439V409C324 403 328 391 317 369C305 348 280 307 258 282C243 266 224 249 200 244V703C132 684 61 672 15 667V638C68 632 75 626 75 570V107C75 42 69 40 9 32V0H266V32C208 40 200 42 200 107V215C203 215 207 214 210 213C215 213 221 207 230 195C274 124 330 34 359 -1L535 0Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.694,3.132)"><path d="M148 517C188 517 220 549 220 587C220 627 188 657 149 657C111 657 78 627 78 587C78 549 111 517 148 517ZM32 388C86 379 93 377 93 305V117C93 52 92 -12 89 -71C87 -105 83 -130 77 -142C70 -153 46 -160 2 -162C-12 -162 -22 -173 -22 -189C-22 -221 4 -244 18 -244C30 -244 38 -240 53 -229C77 -212 153 -128 193 -33C212 13 221 52 221 129V454C157 439 92 425 32 418V388Z"></path></g></svg>  = 125, relationship between critical wave velocity <svg height="9.09935pt" id="M83" 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> and flow <svg height="8.97276pt" id="M84" 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 the condition of different highway grades.</div>

Journal of Advanced Transportation

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Figure 8

Figure 8: An Analysis of the Catastrophe Model and Catastrophe Characteristics of Traffic Flow Based on Cusp Catastrophe Theory 