Complex Dynamical Behaviors of a Fractional-Order System Based on a Locally Active Memristor

<div class="floats-full-page floats-full-page-other"><h2>Table 1</h2><div class="floats-full-page-caption"><div>The eigenvalues as <span class="nowrap"><svg height="15.535pt" id="M77" style="vertical-align:-3.9436pt" version="1.1" viewbox="-0.0498162 -11.5914 109.129 15.535" width="109.129pt" 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="M475 445L452 468C423 436 401 426 385 426S352 427 305 436C268 443 216 448 185 448C156 448 128 425 102 382C89 360 77 338 64 304L89 291C117 340 143 380 190 380C214 380 268 376 295 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(.0091,0,0,-0.0091,10.973,-5.741)"><path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,10.647,3.784)"><path d="M245 635C92 635 37 457 37 312C37 149 91 -12 244 -12C395 -12 449 166 449 312C449 469 395 635 245 635ZM243 598C332 598 358 454 358 312C358 173 334 26 245 26C158 26 128 174 128 313S152 598 243 598Z"></path></g><g transform="matrix(.013,0,0,-0.013,18.825,0)"><path d="M535 230V280H52V230H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,29.362,0)"><path d="M475 445L452 468C423 436 401 426 385 426S352 427 305 436C268 443 216 448 185 448C156 448 128 425 102 382C89 360 77 338 64 304L89 291C117 340 143 380 190 380C214 380 268 376 295 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(.0091,0,0,-0.0091,35.511,3.132)"><path d="M245 635C92 635 37 457 37 312C37 149 91 -12 244 -12C395 -12 449 166 449 312C449 469 395 635 245 635ZM243 598C332 598 358 454 358 312C358 173 334 26 245 26C158 26 128 174 128 313S152 598 243 598Z"></path></g><g transform="matrix(.013,0,0,-0.013,43.362,0)"><path d="M535 230V280H52V230H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,53.899,0)"><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><g transform="matrix(.013,0,0,-0.013,60.139,0)"><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><g transform="matrix(.0091,0,0,-0.0091,64.637,-5.741)"><path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z"></path></g><g transform="matrix(.013,0,0,-0.013,73.215,0)"><path d="M531 285V335L57 550V494L473 310L57 127V71L531 285ZM531 -40V10H57V-40H531Z"></path></g><g transform="matrix(.013,0,0,-0.013,84.478,0)"><path d="M456 178V225H360V632H320C217 496 115 347 20 206V178H280V106C280 40 276 34 189 27V0H445V27C364 34 360 39 360 106V178H456ZM280 225H82C149 335 214 431 278 520H280V225Z"></path></g><g transform="matrix(.013,0,0,-0.013,90.718,0)"><path d="M452 333C452 398 425 448 375 448C329 448 235 404 140 292H138L229 683C233 701 234 712 225 712C208 712 149 686 66 677L64 652H97C135 652 140 651 129 598L38 167C23 96 29 57 44 33C60 7 98 -12 132 -12C169 -12 232 3 290 41C383 102 452 223 452 333ZM365 316C365 199 308 87 239 49C221 39 200 35 183 35C137 35 99 70 112 163C116 191 123 215 129 233C190 316 290 392 330 392C348 392 365 372 365 316Z"></path></g><g transform="matrix(.013,0,0,-0.013,96.82,0)"><path d="M368 703H309L44 -163H104L368 703Z"></path></g><g transform="matrix(.013,0,0,-0.013,102.181,0)"><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></svg>.</span></div></div><div class="floats-full-page-content"><table class="table-group" id="tab1"><tr><td><table class="table"><tr><td class="thead-hr" colspan="4"><hr /></td></tr><tr class="thead"><td class="align_left"><i>z</i><sub>0</sub></td><td class="align_center">(−<i>∞</i>, −0.618)</td><td class="align_center">(−0.3299, 0.3299)</td><td class="align_center">(0.3299, 1.618)</td></tr><tr><td class="thead-hr" colspan="4"><hr /></td></tr><tr><td class="align_left"><i>λ</i><sub>1</sub></td><td class="align_center"><i>λ</i><sub>1</sub> &lt; 0</td><td class="align_center"><i>λ</i><sub>1</sub> &gt; 0</td><td class="align_center"><i>λ</i><sub>1</sub> &lt; 0</td></tr><tr><td class="align_left"><i>λ</i><sub>2</sub></td><td class="align_center"><i>λ</i><sub>2</sub> &lt; 0</td><td class="align_center"><i>λ</i><sub>2</sub> &gt; 0</td><td class="align_center"><i>λ</i><sub>2</sub> &gt; 0</td></tr><tr><td class="align_left"><i>λ</i><sub>3</sub></td><td class="align_center"><i>λ</i><sub>3</sub> &lt; 0</td><td class="align_center"><i>λ</i><sub>3</sub> &gt; 0</td><td class="align_center"><i>λ</i><sub>3</sub> &gt; 0</td></tr><tr><td class="align_left">Equilibrium</td><td class="align_center"><i>E</i><sub>1</sub></td><td class="align_center"><i>E</i><sub>2</sub></td><td class="align_center"><i>E</i><sub>3</sub></td></tr><tr class="table-tr"><td colspan="4"><hr class="tbody-hr" /></td></tr></table></td></tr></table></div></div>

Table 1 | Complex Dynamical Behaviors of a Fractional-Order System Based on a Locally Active Memristor

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Table 1: Complex Dynamical Behaviors of a Fractional-Order System Based on a Locally Active Memristor

description

Table 1

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