An Alternate Iterative Differential Evolution Algorithm for Parameter Identification of Chaotic Systems

<table class="table-group" id="tab6"><tr><td><table class="table"><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr class="thead"><td align="left">Methods</td><td align="center">Index</td><td align="center">Best</td><td align="center">Mean  </td><td align="center">Worst</td></tr><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr><td align="left" rowspan="4"> AIDE </td><td align="center"><span style="width: 6.7023ptpx;"><svg height="9.4556pt" id="M324" style="vertical-align:-0.2063894pt" version="1.1" viewbox="-0.0498162 -9.24921 6.7023 9.4556" width="6.7023pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,1.083,-.222)"><path d="M470 557C393 591 314 624 246 666H224C156 624 76 591 0 557L12 532C86 550 163 573 235 596C309 572 384 550 458 532L470 557Z" id="g119-17"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="470" vert-adv-y="470"></glyph.data></g><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" id="g113-98"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="506" vert-adv-y="506"></glyph.data></g></svg></span></td><td align="center"> 9.990801271058711</td><td align="center">9.998131753034325</td><td align="center">9.989687785636363 </td></tr><tr><td align="center"><span style="width: 6.21949ptpx;"><svg height="12.783pt" id="M325" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -12.5766 6.21949 12.783" width="6.21949pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,-.463,-3.549)"><path d="M470 557C393 591 314 624 246 666H224C156 624 76 591 0 557L12 532C86 550 163 573 235 596C309 572 384 550 458 532L470 557Z" id="g119-17"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="470" vert-adv-y="470"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,0,0)"><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" id="g113-99"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="469" vert-adv-y="469"></glyph.data></g></svg></span></td><td align="center"> 28.003818708942255</td><td align="center">28.000608072179272</td><td align="center">28.002414544105758 </td></tr><tr><td align="center"><span style="width: 5.39742ptpx;"><svg height="9.4556pt" id="M326" style="vertical-align:-0.2063894pt" version="1.1" viewbox="-0.0498162 -9.24921 5.39742 9.4556" width="5.39742pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,.3,-.222)"><path d="M470 557C393 591 314 624 246 666H224C156 624 76 591 0 557L12 532C86 550 163 573 235 596C309 572 384 550 458 532L470 557Z" id="g119-17"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="470" vert-adv-y="470"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M383 397C383 424 344 448 299 448C244 448 172 409 132 375C66 319 23 227 23 146C23 42 74 -12 146 -12C208 -12 298 30 359 103L343 124C315 95 248 48 192 48C145 48 111 85 111 163C111 228 129 294 151 330C171 363 201 401 241 401C275 401 302 384 325 356C332 347 339 344 348 348C373 360 383 381 383 397Z" id="g113-100"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="406" vert-adv-y="406"></glyph.data></g></svg></span></td><td align="center"> 2.667512761713986</td><td align="center">2.666799322681526</td><td align="center">2.667073063185854 </td></tr><tr><td align="center"><span style="width: 5.99765ptpx;"><svg height="10.5647pt" id="M327" style="vertical-align:-1.928801pt" version="1.1" viewbox="-0.0498162 -8.6359 5.99765 10.5647" width="5.99765pt" 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="M429 650H175L169 622C251 614 259 612 244 532L174 152C163 91 152 37 135 -6C109 -72 67 -101 23 -113L33 -144C45 -143 73 -134 102 -119C186 -76 229 -1 254 133L327 532C341 609 347 613 423 622L429 650Z" id="g113-75"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="452" vert-adv-y="452"></glyph.data></g></svg></span></td><td align="center"> 0.0077</td><td align="center">0.0082</td><td align="center">0.0085 </td></tr><tr class="table-tr"><td colspan="5"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Statistical results of AIDE for three-dimensional parameter identification of Lorenz system with noise. 

Discrete Dynamics in Nature and Society

tab6

Table 6

Table 6: An Alternate Iterative Differential Evolution Algorithm for Parameter Identification of Chaotic Systems 