Hopf Bifurcation and Turing Instability Analysis for the Gierer–Meinhardt Model of the Depletion Type

<div>(a) The stable limit cycle of (<a href="https://static.hindawi.com/articles/ddns/volume-2020/5293748/figures/#EEq4">4</a>) becomes unstable for (<a href="https://static.hindawi.com/articles/ddns/volume-2020/5293748/figures/#EEq3">3</a>) for <span class="nowrap"><svg height="11.7782pt" id="M287" style="vertical-align:-3.42938pt" version="1.1" viewbox="-0.0498162 -8.34882 86.9823 11.7782" width="86.9823pt" 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="M548 455L523 469C505 448 490 439 461 439C416 439 374 447 316 447C144 447 23 310 23 161C23 47 89 -12 179 -12C312 -12 429 106 429 244C429 303 419 344 368 386L371 388C404 383 440 378 474 378C507 378 530 411 548 455ZM350 274C350 191 308 25 198 25C144 25 108 75 108 157C108 264 170 395 276 395C296 395 320 384 333 360C347 334 350 316 350 274Z"></path></g><g transform="matrix(.013,0,0,-0.013,10.979,0)"><path d="M535 323V373H52V323H535ZM535 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Discrete Dynamics in Nature and Society

fig6

Figure 6

Figure 6: Hopf Bifurcation and Turing Instability Analysis for the Gierer–Meinhardt Model of the Depletion Type 