Some Novel Complex Dynamic Behaviors of a Class of Four-Dimensional Chaotic or Hyperchaotic Systems Based on a Meshless Collocation Method

<div>Phase portraits of Experiment 1 with <span class="nowrap"><svg height="10.8649pt" id="M109" style="vertical-align:-1.57657pt" version="1.1" viewbox="-0.0498162 -9.28833 109.931 10.8649" width="109.931pt" 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 97L471 123C436 91 401 65 392 65C388 65 384 74 390 106C414 239 444 378 457 429L455 433C444 433 429 436 416 439C392 444 368 448 344 448C281 448 204 415 152 376C71 315 23 205 23 103C23 21 57 -12 85 -12C114 -12 149 6 185 34C231 70 285 119 329 183H331L309 81C292 0 308 -12 326 -12C350 -12 421 24 483 97ZM374 387C370 363 356 291 345 261C315 193 181 50 139 50C124 50 110 71 110 118C110 224 153 331 218 379C238 394 271 402 301 402C329 402 359 394 374 387Z"></path></g><g transform="matrix(.013,0,0,-0.013,10.212,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,21.475,0)"><path d="M412 140C382 77 369 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268 376 295 373C320 370 344 371 362 374L70 101C32 65 23 36 23 18C23 5 27 -3 31 -8C36 -8 39 -6 42 -1C52 15 67 31 80 40S110 49 143 33C195 8 257 -20 290 -20C339 -20 382 11 439 129L416 148C366 74 334 55 305 55C278 55 236 68 203 81C169 94 141 100 122 96C205 170 348 308 411 376L475 445Z"></path></g><g transform="matrix(.013,0,0,-0.013,30.09,0)"><path d="M535 230V280H52V230H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,40.626,0)"><path d="M689 332C689 394 670 448 646 448C620 448 597 421 597 396C597 386 600 381 608 372C619 359 620 334 620 315C620 150 538 45 454 45C414 45 386 67 386 122C386 138 388 158 394 180L457 426L452 432L377 416L315 156C302 100 259 45 216 45C176 45 148 67 148 122C148 133 152 158 156 180C162 212 173 259 194 332C201 357 206 384 206 405C206 430 198 448 174 448C125 448 66 406 23 342L43 319C84 368 110 383 121 383C126 383 128 382 128 377C128 370 127 359 122 343C99 268 84 204 77 156C74 137 70 111 70 104C70 25 125 -12 180 -12C228 -12 276 12 319 50C338 8 378 -12 418 -12C549 -12 689 166 689 332Z"></path></g></svg> plane; <svg height="12.5794pt" id="M116" style="vertical-align:-3.29107pt" version="1.1" viewbox="-0.0498162 -9.28833 21.2526 12.5794" width="21.2526pt" 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="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z"></path></g><g transform="matrix(.013,0,0,-0.013,4.498,0)"><path d="M530 686C535 705 530 712 521 712C504 712 448 684 359 674L358 648H393C437 648 439 646 429 593L400 435C372 447 345 448 332 448C286 448 194 414 144 373C68 311 23 203 23 111C23 26 57 -12 91 -12C120 -12 147 3 188 29C227 54 290 102 341 170H343L322 71C308 6 320 -12 341 -12C373 -12 442 27 501 96L485 120C455 91 422 67 408 67C401 67 401 76 404 91C440 294 479 473 530 686ZM387 375L355 241C326 187 200 53 142 53C126 53 109 73 109 130C109 217 154 337 218 381C240 396 265 404 297 404S372 390 387 375Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,11.648,3.132)"><path d="M290 377C321 398 342 415 358 430C378 450 389 473 389 502C389 578 329 635 238 635H237C184 635 137 610 109 578L64 515L88 493C112 529 154 573 208 573S303 542 303 482C303 409 233 370 141 341L149 308C165 313 190 319 215 319C272 319 341 283 341 193C342 98 292 43 222 43C163 43 122 72 96 94C88 101 79 100 70 94C61 87 47 73 46 60C44 47 48 37 62 23C76 10 118 -12 165 -12C238 -12 430 62 430 223C430 297 379 359 290 375V377Z"></path></g><g transform="matrix(.013,0,0,-0.013,16.594,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z"></path></g></svg> on <svg height="10.4342pt" id="M117" style="vertical-align:-3.4294pt" version="1.1" viewbox="-0.0498162 -7.0048 50.385 10.4342" width="50.385pt" 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="M556 393C556 426 537 448 514 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Complexity

fig9

Figure 9

Figure 9: Some Novel Complex Dynamic Behaviors of a Class of Four-Dimensional Chaotic or Hyperchaotic Systems Based on a Meshless Collocation Method 