Hopf Bifurcation Analysis and Chaos Control of a Chaotic System without <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.3155003pt" id="M1" height="15.4095pt" version="1.1" viewBox="-0.0657574 -15.094 8.82982 15.4095" width="8.82982pt"><g transform="matrix(.017,0,0,-0.017,8.001,-3.832)"><path id="g117-4" d="M-70 617L-95 631C-109 602 -124 588 -144 588C-163 588 -180 594 -202 604C-233 618 -248 623 -268 623C-294 623 -326 604 -353 541L-329 524C-313 552 -298 568 -278 568C-267 568 -248 562 -231 554C-203 541 -180 532 -157 532C-128 532 -93 550 -70 617Z"/></g><g transform="matrix(.017,0,0,-0.017,0,0)"><path id="g187-84" 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"/></g></svg>ilnikov Orbits

<table class="figure-group"><tr class="fig-image" id="a"><td><object data="https://static.hindawi.com/articles/ddns/volume-2015/912798/figures/912798.fig.001a.svgz" name="912798.fig.001a" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(a) </b>The trajectories</td></tr><tr class="fig-image" id="b"><td><object data="https://static.hindawi.com/articles/ddns/volume-2015/912798/figures/912798.fig.001b.svgz" name="912798.fig.001b" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(b) </b>Phase graph</td></tr></table>

<div>The trajectories and phase graphs of system (<a href="https://static.hindawi.com/articles/ddns/volume-2015/912798/figures/#EEq1.2">2</a>) with <svg height="8.55521pt" id="M16" style="vertical-align:-0.2063904pt" version="1.1" viewbox="-0.0498162 -8.34882 27.5889 8.55521" width="27.5889pt" 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="M471 456L444 459C426 433 414 430 388 430C324 430 270 434 216 434C103 434 51 374 23 338L43 317C96 366 146 380 221 375L154 109C149 86 147 68 147 52C147 4 168 -12 197 -12C240 -12 291 25 334 71L320 96C295 75 268 58 252 58C238 58 227 79 238 138C251 211 272 296 292 372C310 372 332 368 350 368C391 368 421 369 434 371C444 388 455 413 471 456Z" id="g113-241"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="483" vert-adv-y="483"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,9.914,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z" id="g117-34"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="587" vert-adv-y="587"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,21.177,0)"><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" id="g113-49"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480"></glyph.data></g></svg>.</div>

Discrete Dynamics in Nature and Society

fig1

Figure 1

Figure 1: Hopf Bifurcation Analysis and Chaos Control of a Chaotic System without <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.3155003pt" id="M1" height="15.4095pt" version="1.1" viewBox="-0.0657574 -15.094 8.82982 15.4095" width="8.82982pt"><g transform="matrix(.017,0,0,-0.017,8.001,-3.832)"><path id="g117-4" d="M-70 617L-95 631C-109 602 -124 588 -144 588C-163 588 -180 594 -202 604C-233 618 -248 623 -268 623C-294 623 -326 604 -353 541L-329 524C-313 552 -298 568 -278 568C-267 568 -248 562 -231 554C-203 541 -180 532 -157 532C-128 532 -93 550 -70 617Z"/></g><g transform="matrix(.017,0,0,-0.017,0,0)"><path id="g187-84" 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"/></g></svg>ilnikov Orbits 

Discrete Dynamics in Nature and Society

Hopf Bifurcation Analysis and Chaos Control of a Chaotic System without ilnikov Orbits

Figure 1