Boundedness and Asymptotic Stability for the Solution of Homogeneous Volterra Discrete Equations

<div>Problem (<a href="https://static.hindawi.com/articles/ddns/volume-2018/6935069/figures/#EEq3.32">43</a>)–(<a href="https://static.hindawi.com/articles/ddns/volume-2018/6935069/figures/#EEq3.35">46</a>): vanishing <span class="nowrap"><svg height="9.39034pt" id="M271" style="vertical-align:-3.42943pt" version="1.1" viewbox="-0.0498162 -5.96091 12.2425 9.39034" width="12.2425pt" 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="M556 393C556 426 537 448 514 448C496 448 478 435 471 420C468 414 462 401 466 394C473 382 480 368 480 346C480 268 392 143 338 67H336C329 163 319 253 309 330S286 448 254 448C215 448 160 383 127 337L143 311C167 344 200 373 208 373S222 365 229 320C246 214 264 66 268 -20C219 -83 131 -171 17 -239L25 -261L137 -235C248 -110 273 -79 335 8C384 77 481 215 520 287C544 332 556 363 556 393Z" id="g113-122"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.942,3.132)"><path d="M504 89L488 119C453 85 428 69 416 69C408 69 405 75 412 102L462 304C492 438 460 451 436 451S388 441 356 423C311 397 229 336 170 256H168L189 340C208 418 200 451 177 451C144 451 82 413 24 352L40 322C65 345 98 369 108 369C114 369 119 363 112 335L28 -3L36 -12C54 -3 83 4 112 10C125 73 138 122 153 174C205 258 328 382 376 382C395 382 399 369 384 305L330 93C312 25 323 -12 351 -12C378 -12 439 21 504 89Z" id="g50-111"></path></g></svg>.</span></div>

Discrete Dynamics in Nature and Society

fig3

Figure 3

Figure 3: Boundedness and Asymptotic Stability for the Solution of Homogeneous Volterra Discrete Equations 