Modified Hyperspheres Algorithm to Trace Homotopy Curves of Nonlinear Circuits Composed by Piecewise Linear Modelled Devices

<table class="table-group" width="800px"><tr class="fig-image" id="a"><td><img alt="938598.fig.0011a" src="https://static.hindawi.com/articles/tswj/volume-2014/938598/figures/938598.fig.0011a.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(a) </b>Homotopy path for initial point <svg height="12.2868pt" id="M147" style="vertical-align:-3.2637pt" version="1.1" viewbox="0 -9.0231 14.3326 12.2868" width="14.3326pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path d="M699 368C699 549 574 666 407 666C186 666 23 488 23 277C23 113 129 -3 288 -13L307 -26C431 -111 501 -139 533 -147C559 -154 613 -163 658 -164L666 -141C597 -111 507 -66 430 -11L416 -1C580 42 699 190 699 368ZM601 371C601 227 518 54 381 22L354 40L278 24C175 47 120 145 120 269C120 451 235 631 398 631C540 631 601 521 601 371Z" id="g113-82"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="722" vert-adv-y="722"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,9.714,3.264)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z" id="g50-50"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g></svg></td></tr></table></td></tr><tr class="fig-image" id="b"><td><img alt="938598.fig.0011b" src="https://static.hindawi.com/articles/tswj/volume-2014/938598/figures/938598.fig.0011b.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(b) </b>Zoom for (a)</td></tr></table></td></tr><tr class="fig-image" id="c"><td><img alt="938598.fig.0011c" src="https://static.hindawi.com/articles/tswj/volume-2014/938598/figures/938598.fig.0011c.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(c) </b>Homotopy path for initial point <svg height="12.2868pt" id="M148" style="vertical-align:-3.2637pt" version="1.1" viewbox="0 -9.0231 14.3326 12.2868" width="14.3326pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path d="M699 368C699 549 574 666 407 666C186 666 23 488 23 277C23 113 129 -3 288 -13L307 -26C431 -111 501 -139 533 -147C559 -154 613 -163 658 -164L666 -141C597 -111 507 -66 430 -11L416 -1C580 42 699 190 699 368ZM601 371C601 227 518 54 381 22L354 40L278 24C175 47 120 145 120 269C120 451 235 631 398 631C540 631 601 521 601 371Z" id="g113-82"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="722" vert-adv-y="722"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,9.714,3.264)"><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" id="g50-51"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g></svg></td></tr></table></td></tr><tr class="fig-image" id="d"><td><img alt="938598.fig.0011d" src="https://static.hindawi.com/articles/tswj/volume-2014/938598/figures/938598.fig.0011d.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(d) </b>Zoom for (c)</td></tr></table></td></tr></table>

<table>Homotopy paths for (<a href="https://static.hindawi.com/articles/tswj/volume-2014/938598/figures/#EEq20">18</a>) projected over <svg height="9.80889pt" id="M145" style="vertical-align:-0.1625805pt" version="1.1" viewbox="0 -9.64631 7.4786 9.80889" width="7.4786pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path d="M529 97L508 118C475 75 449 58 438 58C428 58 421 66 415 104C393 234 374 403 364 496C345 670 307 712 254 712C220 712 174 691 153 669L161 645C176 653 194 658 206 658C237 658 261 640 278 562C287 522 290 483 293 434C223 269 110 105 23 9L32 -12C59 -6 85 0 108 7C152 64 251 252 300 366C307 297 315 221 337 82C346 24 363 -12 393 -12C425 -12 475 13 529 97Z" id="g113-233"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="552" vert-adv-y="552"></glyph.data></g></svg>-<svg height="9.4699pt" id="M146" style="vertical-align:-3.37755pt" version="1.1" viewbox="0 -6.09235 10.6746 9.4699" width="10.6746pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0136,0,0,-0.0136,0,0)"><path d="M219 86C216 168 211 250 206 337C201 410 189 448 163 448C131 448 79 396 43 344L60 322C91 359 110 375 118 375S132 358 136 298C141 238 152 81 155 -12H182C242 62 331 177 390 258C435 321 451 360 451 391C450 424 432 448 408 448C390 448 372 435 366 419C362 410 362 401 366 394C373 383 376 367 376 350C376 283 262 138 221 86H219Z" id="g185-40"></path><glyph.data ascent="989" descent="-303" horiz-adv-x="447" vert-adv-y="447"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,6.056,3.264)"><path d="M290 377C321 398 342 415 358 430C378 450 389 473 389 502C389 578 329 635 238 635H237C184 635 137 610 109 578L64 515L88 493C112 529 154 573 208 573S303 542 303 482C303 409 233 370 141 341L149 308C165 313 190 319 215 319C272 319 341 283 341 193C342 98 292 43 222 43C163 43 122 72 96 94C88 101 79 100 70 94C61 87 47 73 46 60C44 47 48 37 62 23C76 10 118 -12 165 -12C238 -12 430 62 430 223C430 297 379 359 290 375V377Z" id="g50-52"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g></svg>.</table>

The Scientific World Journal

fig11

Figure 11

Figure 11: Modified Hyperspheres Algorithm to Trace Homotopy Curves of Nonlinear Circuits Composed by Piecewise Linear Modelled Devices 