Nonlinear dynamics of the media addiction model using the fractal-fractional derivative technique

<div>(a) Displays of addicted individuals <svg height="12.2089pt" id="M298" style="vertical-align:-2.503pt" version="1.1" viewbox="-0.0498162 -9.7059 21.6301 12.2089" width="21.6301pt" 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="M442 495C434 557 427 602 423 639C405 645 348 665 284 665C142 665 55 579 55 469C55 373 127 319 229 267C304 227 348 190 348 131C348 67 309 25 248 25C152 25 93 138 73 202L38 190C45 130 58 46 68 21C81 15 100 7 128 -1C158 -10 193 -15 229 -15C375 -15 472 74 472 188C472 287 400 343 295 394C207 439 171 470 171 525C171 583 212 624 268 624C349 624 387 550 407 487L442 495Z"></path></g><g transform="matrix(.013,0,0,-0.013,6.59,0)"><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,-0.013,11.088,0)"><path d="M430 689C430 695 425 700 413 700C377 700 332 667 290 635C232 640 213 677 213 696C213 713 220 724 226 732L209 744C166 731 135 700 135 674C135 636 184 601 255 599C144 503 23 345 23 181C23 82 68 44 135 20C156 12 177 7 202 2C238 -5 252 -25 252 -53C252 -98 211 -144 192 -164L214 -187C257 -152 328 -92 328 -19C328 31 298 58 251 70C230 75 208 81 189 88C142 105 108 134 108 208C108 346 202 512 303 595C352 599 430 626 430 689Z"></path></g><g transform="matrix(.013,0,0,-0.013,16.979,0)"><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> (b) Displays of recovered individuals <svg height="12.2089pt" id="M299" style="vertical-align:-2.503pt" version="1.1" viewbox="-0.0498162 -9.7059 22.6218 12.2089" width="22.6218pt" 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 173C517 129 499 97 479 75C456 50 421 43 369 43C331 43 297 45 279 53C259 63 255 87 255 135V309H322C407 309 420 305 433 233H469V434H433C420 364 406 359 322 359H255V571C255 604 259 606 296 606H344C400 606 427 599 444 581C462 563 475 530 484 495L521 500C517 562 512 632 511 650H40V615C111 609 121 604 121 517V133C121 48 111 42 26 35V0H536C544 30 564 121 571 166L535 173Z"></path></g><g transform="matrix(.013,0,0,-0.013,7.581,0)"><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,-0.013,12.079,0)"><path d="M430 689C430 695 425 700 413 700C377 700 332 667 290 635C232 640 213 677 213 696C213 713 220 724 226 732L209 744C166 731 135 700 135 674C135 636 184 601 255 599C144 503 23 345 23 181C23 82 68 44 135 20C156 12 177 7 202 2C238 -5 252 -25 252 -53C252 -98 211 -144 192 -164L214 -187C257 -152 328 -92 328 -19C328 31 298 58 251 70C230 75 208 81 189 88C142 105 108 134 108 208C108 346 202 512 303 595C352 599 430 626 430 689Z"></path></g><g transform="matrix(.013,0,0,-0.013,17.97,0)"><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> using a another numerical approach for decreasing fractional-order <svg height="6.1673pt" id="M300" style="vertical-align:-0.2063904pt" version="1.1" viewbox="-0.0498162 -5.96091 7.51131 6.1673" width="7.51131pt" 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="M545 106L524 126C493 85 467 65 455 65C438 65 427 113 405 238C448 295 498 362 543 439L533 448L478 435C453 386 423 331 398 295H395C370 404 347 448 282 448C169 448 23 309 23 153C23 54 65 -12 128 -12C203 -12 283 70 339 155H341C360 29 380 -12 411 -12C444 -12 491 11 545 106ZM333 204C265 95 210 54 169 54C137 54 113 96 113 171C113 302 191 405 252 405C301 405 318 306 333 204Z"></path></g></svg> and fixed fractal-dimension <span class="nowrap"><svg height="11.7782pt" id="M301" style="vertical-align:-3.42938pt" version="1.1" viewbox="-0.0498162 -8.34882 29.1939 11.7782" width="29.1939pt" 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="M583 333C583 398 556 448 506 448C465 448 403 428 328 383C238 329 167 252 115 162C110 186 106 208 106 232C106 311 133 374 194 424L176 448C81 390 29 315 29 201C29 144 44 95 69 62C43 -14 29 -91 29 -141C29 -196 67 -261 115 -261C181 -261 246 -214 246 -126C246 -76 228 -51 192 -8C163 27 152 43 138 86C174 178 224 250 294 305C361 358 425 392 461 392C479 392 496 372 496 316C496 199 462 38 386 38C366 38 340 66 324 108C322 114 307 116 298 111C277 99 270 84 270 65C270 29 304 -12 358 -12C384 -12 423 3 469 41C535 96 583 223 583 333ZM198 -142C198 -181 173 -205 149 -205C122 -205 94 -174 94 -121C94 -92 101 -42 114 6C157 -37 198 -83 198 -142Z"></path></g><g transform="matrix(.013,0,0,-0.013,11.51,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,22.773,0)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z"></path></g></svg>.</span></div>

Complexity

fig11

Figure 11

Figure 11: Nonlinear dynamics of the media addiction model using the fractal-fractional derivative technique 