Global Dynamics, Bifurcation Analysis, and Chaos in a Discrete Kolmogorov Model with Piecewise-Constant Argument

<table class="table-group" id="tab2"><tr><td><table class="table"><tr><td class="thead-hr" colspan="2"><hr/></td></tr><tr class="thead"><td class="align_left">Properties</td><td class="align_center">Respective parametric conditions</td></tr><tr><td class="thead-hr" colspan="2"><hr/></td></tr><tr><td class="align_left">Saddle</td><td class="align_center"><span style="width: 163.565ptpx;"><svg height="13.1379pt" id="M42" style="vertical-align:-3.18151pt" version="1.1" viewbox="-0.0498162 -9.95639 163.565 13.1379" width="163.565pt" 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="M162 -163V703H101V-163H162Z"></path></g><g transform="matrix(.013,0,0,-0.013,3.419,0)"><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 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<div>Topological classifications at fixed point <span class="nowrap"><svg height="10.7866pt" id="M41" style="vertical-align:-2.150701pt" version="1.1" viewbox="-0.0498162 -8.6359 9.52083 10.7866" width="9.52083pt" 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="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"></path></g></svg>.</span></div>

Mathematical Problems in Engineering

tab2

Table 2

Table 2: Global Dynamics, Bifurcation Analysis, and Chaos in a Discrete Kolmogorov Model with Piecewise-Constant Argument 