Dynamic Behaviors and the Equivalent Realization of a Novel Fractional-Order Memristor-Based Chaotic Circuit

<div>Phase diagrams of the integer-order system and fractional-order system: (a) <svg height="12.4646pt" id="M116" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -12.2582 40.4794 12.4646" width="40.4794pt" 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="M541 160L512 170C485 116 462 88 439 67C411 41 376 35 318 35C272 35 238 37 224 48C207 61 205 85 212 121L290 533C305 611 308 615 391 622L397 650H139L133 622C217 615 221 612 206 533L126 118C111 41 103 34 23 26L17 0H474C489 31 528 124 541 160Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.185,-5.741)"><path d="M547 100L523 123C489 76 461 62 452 62C442 62 433 71 427 109C405 243 387 408 378 495C360 666 322 710 263 710C230 710 182 688 161 667L170 639C184 646 203 651 218 651C247 651 272 634 288 562C297 521 300 485 304 436C230 267 111 104 24 11L33 -12L116 6C163 73 263 255 311 362L347 84C355 26 373 -12 406 -12C440 -12 489 12 547 100Z"></path></g><g transform="matrix(.013,0,0,-0.013,16.53,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,27.793,0)"><path d="M412 140C382 77 369 73 315 73H129L270 222C362 320 402 379 402 466C402 571 322 635 234 635C177 635 130 609 99 576L42 495L64 475C90 514 133 568 201 568C274 568 318 519 318 435C318 349 255 267 193 193C144 135 87 78 32 23V0H405C417 45 427 89 440 131L412 140Z"></path></g><g transform="matrix(.013,0,0,-0.013,34.033,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z"></path></g></svg> mH and (b) <svg height="12.4646pt" id="M117" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -12.2582 40.4794 12.4646" width="40.4794pt" 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="M541 160L512 170C485 116 462 88 439 67C411 41 376 35 318 35C272 35 238 37 224 48C207 61 205 85 212 121L290 533C305 611 308 615 391 622L397 650H139L133 622C217 615 221 612 206 533L126 118C111 41 103 34 23 26L17 0H474C489 31 528 124 541 160Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.185,-5.741)"><path d="M547 100L523 123C489 76 461 62 452 62C442 62 433 71 427 109C405 243 387 408 378 495C360 666 322 710 263 710C230 710 182 688 161 667L170 639C184 646 203 651 218 651C247 651 272 634 288 562C297 521 300 485 304 436C230 267 111 104 24 11L33 -12L116 6C163 73 263 255 311 362L347 84C355 26 373 -12 406 -12C440 -12 489 12 547 100Z"></path></g><g transform="matrix(.013,0,0,-0.013,16.53,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,27.793,0)"><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,-0.013,34.034,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z"></path></g></svg> mH.</div>

Complexity

fig9

Figure 9

Figure 9: Dynamic Behaviors and the Equivalent Realization of a Novel Fractional-Order Memristor-Based Chaotic Circuit 