Analysis of the Dynamical Properties of Discrete Predator-Prey Systems with Fear Effects and Refuges

<div>Hopf bifurcation stabilization regions of system (<a href="https://static-preview.hindawi.com/articles/ddns/volume-2024/9185585/figures/#EEq3">3</a>) at <span class="nowrap"><svg height="10.8649pt" id="M307" style="vertical-align:-1.57657pt" version="1.1" viewbox="-0.0498162 -9.28833 434.582 10.8649" width="434.582pt" 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="M499 88L487 113C459 86 422 65 413 65C403 65 403 74 409 98L461 318C487 426 460 448 431 448C408 448 383 441 352 424C305 398 223 344 157 257H155L243 674C249 702 249 712 240 712C227 712 170 680 87 673L82 648H117C155 648 162 644 150 590L23 -4L30 -12C55 -4 81 3 105 8C113 53 131 150 143 187C199 281 323 387 372 387C390 387 393 369 380 311L328 86C313 19 319 -12 347 -12C379 -12 442 24 499 88Z"></path></g><g transform="matrix(.013,0,0,-0.013,10.34,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g 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Discrete Dynamics in Nature and Society

fig9

Figure 9

Figure 9: Analysis of the Dynamical Properties of Discrete Predator-Prey Systems with Fear Effects and Refuges 