<svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-4.488899pt" id="M1" height="16.5945pt" version="1.1" viewBox="-0.0657574 -12.1056 28.3256 16.5945" width="28.3256pt"><g transform="matrix(.017,0,0,-0.017,0,0)"><path id="g199-9" d="M816 658L786 699C759 680 740 670 717 662C686 651 661 649 638 649C555 649 495 699 388 699C263 699 199 617 199 545C199 477 245 418 330 418C378 418 409 432 436 461L407 496C388 479 370 473 350 473C319 473 290 493 290 545C290 593 330 644 384 644C457 644 484 569 598 569V567C470 452 437 385 386 305C271 265 187 232 126 175C91 142 65 101 65 56C65 3 105 -21 169 -21C312 -21 457 152 534 295C549 300 584 310 607 318C575 267 524 175 524 96C524 33 557 -18 646 -18C683 -18 715 -5 750 18C786 43 822 79 861 139L819 165C741 68 702 41 673 41C654 41 644 50 644 69C644 124 717 254 811 388C997 441 1154 526 1154 636C1154 676 1128 699 1077 699C972 699 813 590 660 392C648 387 587 368 571 365C640 500 710 575 792 639L816 658ZM875 473C934 577 1016 644 1047 644C1059 644 1065 638 1065 627C1065 553 944 487 875 471V473ZM344 225C293 131 218 34 176 34C165 34 156 38 156 54C156 118 244 195 343 227L344 225Z"/></g><g transform="matrix(.012,0,0,-0.012,20.094,4.134)"><path id="g54-33" d="M556 236V289H56V236H556Z"/></g></svg> Index for Stochastic Linear Discrete-Time Systems

<div>The minimum eigenvalue of <svg height="15.3509pt" id="M405" style="vertical-align:-4.2371pt" version="1.1" viewbox="-0.0498162 -11.1138 31.0979 15.3509" width="31.0979pt" 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="M600 480C600 590 528 650 384 650H143L137 622C222 614 225 607 210 531L130 127C113 41 106 36 23 28L17 0H294L300 28C204 36 195 42 212 127L243 284L314 263C327 263 339 263 352 264C465 271 600 337 600 480ZM508 481C508 351 402 304 329 304C289 304 265 311 250 317L295 559C302 594 310 606 323 611C335 616 350 619 367 619C455 619 508 573 508 481Z" id="g113-81"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="617" vert-adv-y="617"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,8.026,-6.899)"><path d="M493 373C493 420 472 451 445 451C421 451 400 435 400 410C400 404 402 400 406 394S417 371 417 350C417 259 317 128 256 55H254C260 126 256 262 238 340C219 424 194 451 163 451C128 451 78 413 24 329L52 302C89 353 106 370 121 370C129 370 137 363 147 336C186 231 196 73 184 -16C152 -88 120 -192 112 -238L130 -257C157 -253 213 -227 231 -213C231 -187 234 -77 240 -23C251 -6 277 30 309 69C424 208 493 299 493 373Z" id="g50-225"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="517" vert-adv-y="517"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,6.656,4.187)"><path d="M389 0V32C297 37 291 46 291 118V635C234 612 176 595 109 583V556L161 554C203 551 207 548 207 497V118C207 46 201 37 110 32V0H389Z" id="g58-47"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,11.088,4.187)"><path d="M655 676H628C608 656 600 650 571 650H156C118 650 114 651 102 676H77C63 615 45 548 24 485L60 486C81 531 97 562 114 580C134 603 148 611 252 611H308L217 127C201 41 196 38 105 32L98 0H384L393 32C300 38 288 41 304 127L393 611H466C553 611 571 604 582 580C592 559 597 530 595 485L630 489C636 548 645 624 655 676Z" id="g50-85"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="673" vert-adv-y="673"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,17.494,0)"><path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z" id="g113-41"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,21.992,0)"><path d="M324 430H196L233 583L223 592L145 529L120 430H54L29 396L31 388H111L56 126C33 15 54 -12 77 -12C137 -12 214 57 250 95L233 119C208 92 155 59 138 59C126 59 120 70 131 125L186 390L298 394L324 430Z" id="g113-117"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="341" vert-adv-y="341"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,26.425,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z" id="g113-42"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data></g></svg>.</div>

Discrete Dynamics in Nature and Society

fig1

Figure 1

Figure 1: <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-4.488899pt" id="M1" height="16.5945pt" version="1.1" viewBox="-0.0657574 -12.1056 28.3256 16.5945" width="28.3256pt"><g transform="matrix(.017,0,0,-0.017,0,0)"><path id="g199-9" d="M816 658L786 699C759 680 740 670 717 662C686 651 661 649 638 649C555 649 495 699 388 699C263 699 199 617 199 545C199 477 245 418 330 418C378 418 409 432 436 461L407 496C388 479 370 473 350 473C319 473 290 493 290 545C290 593 330 644 384 644C457 644 484 569 598 569V567C470 452 437 385 386 305C271 265 187 232 126 175C91 142 65 101 65 56C65 3 105 -21 169 -21C312 -21 457 152 534 295C549 300 584 310 607 318C575 267 524 175 524 96C524 33 557 -18 646 -18C683 -18 715 -5 750 18C786 43 822 79 861 139L819 165C741 68 702 41 673 41C654 41 644 50 644 69C644 124 717 254 811 388C997 441 1154 526 1154 636C1154 676 1128 699 1077 699C972 699 813 590 660 392C648 387 587 368 571 365C640 500 710 575 792 639L816 658ZM875 473C934 577 1016 644 1047 644C1059 644 1065 638 1065 627C1065 553 944 487 875 471V473ZM344 225C293 131 218 34 176 34C165 34 156 38 156 54C156 118 244 195 343 227L344 225Z"/></g><g transform="matrix(.012,0,0,-0.012,20.094,4.134)"><path id="g54-33" d="M556 236V289H56V236H556Z"/></g></svg> Index for Stochastic Linear Discrete-Time Systems 