Rank One Strange Attractors in Periodically Kicked Lorenz System with Time-Delay

<div>Largest Lyapunov exponent <svg height="9.49473pt" id="M539" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -9.28833 7.55047 9.49473" width="7.55047pt" 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="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" id="g50-233"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="571" vert-adv-y="571"></glyph.data></g></svg> versus <svg height="6.20645pt" id="M540" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -6.00005 5.58009 6.20645" width="5.58009pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g 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descent="-369" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,30.014,0)"><path d="M253 635C142 635 71 555 71 471C71 400 113 353 178 316C143 295 107 268 91 252C70 231 46 202 46 157C46 50 132 -12 241 -12C329 -12 442 52 442 168C442 257 379 305 311 343C354 374 380 398 388 407C407 428 417 458 417 487C417 568 348 635 253 635ZM240 600C288 600 340 564 340 481C340 422 314 387 279 360C207 395 148 426 148 499C148 549 181 600 240 600ZM252 23C188 23 129 72 129 163C129 218 162 266 211 298C288 261 360 217 360 144C360 68 312 23 252 23Z" id="g58-54"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g></svg> (a), <svg height="9.01844pt" id="M542" style="vertical-align:-0.2129107pt" version="1.1" viewbox="-0.0498162 -8.80553 42.9038 9.01844" width="42.9038pt" 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="M655 676H628C608 656 600 650 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transform="matrix(.013,0,0,-0.013,28.115,0)"><path d="M117 -12C153 -12 178 12 178 50C178 84 153 110 118 110C84 110 59 84 59 50C59 12 84 -12 117 -12Z" id="g50-47"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="237" vert-adv-y="237"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,31.196,0)"><path d="M462 177V227H365V632H320C216 495 117 351 21 208V177H284V109C284 42 281 39 190 31V0H451V31C369 39 365 42 365 108V177H462ZM284 227H88C156 336 218 430 282 519H284V227Z" id="g58-50"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g></svg>, and <svg height="6.20645pt" id="M544" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -6.00005 5.58009 6.20645" width="5.58009pt" 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="M396 374C396 399 365 451 262 451C173 451 84 405 84 327C84 295 107 257 157 243V241C91 226 24 184 24 119C24 41 92 -12 189 -12C272 -12 344 31 386 91L367 118C325 76 274 50 222 50C163 50 120 84 120 138C120 191 169 218 223 218C247 218 263 217 278 216L312 260L308 267H259C200 267 167 297 167 338S202 414 250 414C297 414 326 387 336 341C338 331 341 328 349 328C361 328 396 349 396 374Z" id="g50-247"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="420" vert-adv-y="420"></glyph.data></g></svg> varying from 0 to 0.4.</div>

Discrete Dynamics in Nature and Society

fig5

Figure 5

Figure 5: Rank One Strange Attractors in Periodically Kicked Lorenz System with Time-Delay 