Rich Dynamics of a Predator-Prey System with Different Kinds of Functional Responses

<div>Bifurcation diagram with respect to birth rate of prey species <svg height="9.25202pt" id="M567" style="vertical-align:-3.29111pt" version="1.1" viewbox="-0.0498162 -5.96091 9.96544 9.25202" width="9.96544pt" 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="M393 379C402 394 400 411 393 422C384 437 365 448 348 448C301 448 237 372 186 285H182L193 335C210 408 205 448 178 448C150 448 80 402 29 344L45 321C80 355 114 373 122 373C128 373 130 365 124 330C106 228 76 98 50 -5L57 -12C82 -5 112 3 132 6L172 203C196 256 234 304 254 329C275 355 293 367 306 367C318 367 330 360 342 348C347 343 355 343 365 350S386 367 393 379Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,4.901,3.132)"><path d="M245 635C92 635 37 457 37 312C37 149 91 -12 244 -12C395 -12 449 166 449 312C449 469 395 635 245 635ZM243 598C332 598 358 454 358 312C358 173 334 26 245 26C158 26 128 174 128 313S152 598 243 598Z"></path></g></svg> of the predator-prey system (<a href="https://static.hindawi.com/articles/complexity/volume-2020/4285294/figures/#EEq19">19</a>) with Beddington–DeAngelis-type response function. 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Complexity

fig9

Figure 9

Figure 9: Rich Dynamics of a Predator-Prey System with Different Kinds of Functional Responses 