A Holling Type II Discrete Switching Host-Parasitoid System with a Nonlinear Threshold Policy for Integrated Pest Management

<div>Periods of period point cycles of system (<a href="https://static.hindawi.com/articles/ddns/volume-2020/9425285/figures/#EEq4">4</a>) with respect to parameters <svg height="6.1673pt" id="M248" style="vertical-align:-0.2063904pt" version="1.1" viewbox="-0.0498162 -5.96091 5.60619 6.1673" width="5.60619pt" 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></svg> and <span class="nowrap"><svg height="6.1673pt" id="M249" style="vertical-align:-0.2063904pt" version="1.1" viewbox="-0.0498162 -5.96091 6.7023 6.1673" width="6.7023pt" 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="M483 97L471 123C436 91 401 65 392 65C388 65 384 74 390 106C414 239 444 378 457 429L455 433C444 433 429 436 416 439C392 444 368 448 344 448C281 448 204 415 152 376C71 315 23 205 23 103C23 21 57 -12 85 -12C114 -12 149 6 185 34C231 70 285 119 329 183H331L309 81C292 0 308 -12 326 -12C350 -12 421 24 483 97ZM374 387C370 363 356 291 345 261C315 193 181 50 139 50C124 50 110 71 110 118C110 224 153 331 218 379C238 394 271 402 301 402C329 402 359 394 374 387Z"></path></g></svg>,</span> where different color intensities represent different periodic values. The other parameters are fixed as follows: <span class="nowrap"><svg height="12.7373pt" id="M250" style="vertical-align:-3.429399pt" version="1.1" viewbox="-0.0498162 -9.3079 318.229 12.7373" width="318.229pt" 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="M570 304C570 398 525 448 414 448C385 448 343 445 312 434L329 511L321 518C297 504 262 482 244 460L233 411C195 397 159 381 128 358L135 332C160 347 189 360 224 373L111 -147C97 -210 84 -218 17 -231L13 -257L254 -247L259 -218L233 -216C183 -212 177 -202 189 -142L218 -1C238 -10 266 -12 283 -12C351 3 429 48 483 105C543 168 570 242 570 304ZM482 289C482 161 380 33 304 33C278 33 248 51 233 69L303 396C326 400 352 403 369 403C428 403 482 380 482 289Z"></path></g><g transform="matrix(.013,0,0,-0.013,11.342,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,22.605,0)"><path d="M241 635C89 635 35 457 35 312C35 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Discrete Dynamics in Nature and Society

fig5

Figure 5

Figure 5: A Holling Type II Discrete Switching Host-Parasitoid System with a Nonlinear Threshold Policy for Integrated Pest Management 