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Liao X., Wang L., Yu P. Ч Stability of Dynamical Systems, Vol. 5
Liao X., Wang L., Yu P. Ч Stability of Dynamical Systems, Vol. 5

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Ќазвание: Stability of Dynamical Systems, Vol. 5

јвторы: Liao X., Wang L., Yu P.

јннотаци€:

The main purpose of developing stability theory is to examine dynamic responses of a system to disturbances as the time approaches infinity. It has been and still is the object of intense investigations due to its intrinsic interest and its relevance to all practical systems in engineering, finance, natural science and social science. This monograph provides some state-of-the-art expositions of major advances in fundamental stability theories and methods for dynamic systems of ODE and DDE types and in limit cycle, normal form and Hopf bifurcation control of nonlinear dynamic systems.

Х Presents comprehensive theory and methodology of stability analysis
Х Can be used as textbook for graduate students in applied mathematics, mechanics, control theory, theoretical physics, mathematical biology, information theory, scientific computation
Х Serves as a comprehensive handbook of stability theory for practicing aerospace, control, mechanical, structural, naval and civil engineers


язык: en

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 2007

 оличество страниц: 545

ƒобавлена в каталог: 23.05.2008

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
$Z_2$-equivariant vector field      609
$Z_2$-symmetry      611 613
$\omega$-limit orbit      244 256
$\omega$-limit point      145
$\omega$-limit set      169 244 256 494
2-D Henon map      651Ч656
2-D lifting surface      658
2-D supersonic lifting surface      658
3-D Henon map      646 656 657
Abed      631
Absolute integrability      215
Absolute stability      220 389 394 420 421 423 424 434Ч436 439 440 442 443 452 454 459 463 469 471 481
Absolutely stable      392Ч394 396Ч399 402Ч419 421Ч433 435Ч447 449Ч451 453Ч456 458 459 461Ч468 470Ч472 474 475 478Ч485
Absolutely stable with respect to      421 423Ч430 435Ч443 456 472 474 475 483
Absolutely stable within (in) the Hurwitz angle      392 396 397 402Ч404 406Ч412 418 419
Activation function      491 502 507 515 541 571
Aerodynamic nonlinearities      658
Aeroelastic model      658
AizemanТs conjecture      241
Algebraic multiplicity      40 42
Anti-bifurcation control      651 652
Anti-control      640 646 649 656
Anti-controlling bifurcation      626 640
Anti-controlling Hopf bifurcation      646
Associative memory      487 491 530 532 534
Asymptotic behavior      22 26 209 495
Asymptotic equivalence      167 208 209
Asymptotic stability      24 28 32 33 35 36 82 83 111 112 123Ч125 139 140 143 145 162 163 173 176 177 185 218 227 228 237 245 379 403 489 532 550 552 553 566
Asymptotically equivalent      209 211 217 218
Asymptotically stable      24Ч27 31 36 81 82 94 95 106Ч108 110 123 125 127 139Ч141 143Ч146 148 150 169 171 172 174 176 185Ч187 219 225 227 238 239 287 323 336 337 341 356 357 359Ч361 364 366 369 373 374 378Ч380 393 403 496 499Ч501 530 532 551 553Ч557 586
Asymptotically stable cone      357 361 380 381 383 384
Asymptotically stable with respect to      106Ч108 225 227 228 232 233 237
Asynchronous machine      604
Attractive      22 24Ч26 28 81 82 135 136 141 142 151 186 224 237 489 494 499
Attractive with respect to      105 106 108 225 227
Attractive, basin      145 165
Attractive, space      447
Automatic control      35 301 321 322 389 392
Autonomous      31 32 146 157 463 601
Autonomous nonlinear system      241
Autonomous system      31 112 136 145 167 237 615
Averaging method      591
Banach space      297 470 547 663
BarabashinЧKrasovskii theorem      171 176
Bautin      609
Bhatia      447
Bidirectional associative memory (BAM) model      532 537
Bidirectional neural network      487 491 530 534 540
Bidirectional system      530
Bifurcation, control      593 594 627 640
Bifurcation, controller      645
Bifurcation, parameter      591 592 606 608 627 630 643 651 656
Bifurcation, point      640 641
Bifurcation, theory      643 644
Bilinear operator      663
Biomathematics      341
Birkhoff limit set      167
Brown fixed point theorem      565
Brusselator model      602 604
Bulgakov problem      389
Burton      420
Canonical form      596 607 637
Catastrophic type of flutter boundary      658
Cauchy matrix solution      36 77 78 80 83 86 88 90 92Ч95 97Ч99 105 204 205 207 232 286 309 310 314 367Ч369 374
Cauchy problem      21 30 263 323 342
Cauchy sequence      297
CauchyТs argument principle      61
Center      599 601 609
Center manifold      591 595 614 622Ч624 642 644 657 662 663 665 667
Center manifold, reduction      643 663
Center manifold, theory      591 594 597 606 614 617 642
Centrifugal governor      389 390
Chaos      469 491 591 593 627 651 657
Chaos, control      593 627 656
Chaos, synchronization      459 460 467
Chaotic attractor      188 189 629 654
Chaotic motion      491 593 627 629 654
Characteristic curve      68Ч70 72Ч75
Characteristic equation      356 357 379 380 406 472 663
Characteristic function      661
Characteristic polynomial      631 636 642 643 662
Chen      189 459 466
Chen system      467 469
Chua      466 467 563
Closed orbit      138 647
Closed-loop      70 71 73Ч75 389 631 632
CNF (conventional normal form)      614 621 622 627 632
CNN (cellular neural network)      491 563Ч566 568 570 586Ч588
Cohen      551
Compact      168 169 180 198
Compact, convex set      565
Compact, set      148 168 169 180 201
Comparability theory      171
Comparison method      176 177 367
Comparison principle      167 172 209 350
Comparison theorem      14 15 128 176 190
Complex center      601
Complex conjugate      593 640Ч643 647Ч649 653
Concomitant      600 601
Conditional stability      167 218
Conditionally asymptotically stable      219
Conditionally stable      218 219
Constant sign function      4
Constant variation formula      437
Continuous system      594 627
Control parameter      591 615 629
Convex      361 362 383Ч387
Convex set      384 565
Critical control system      392
Critical Lurie control system      434
Critical point      591 593 599 601Ч603 606 615 626 627 629Ч632 638 641 651 660
Curran      466
DDE (delay differential equation)      285 541
Degenerate Hopf bifurcation      597 609
Delay differential equation      285 541
Delay logistic equation      646 651
Delay logistic map      646 653
Delayed differential difference equation      322 363
Delayed neural system      541 547
Delayed system      325
Difference equation      321
Differential difference equation      321Ч324 333 338 363 368
Differential inequality      13 350 351 354 355 367 372
Dini derivative      1 10 11 13 271 332 339 345 527 537 556 567 573
Dini derivative inequality      350
Direct control system      392 394 399 402 435
Discrete map      591 594 627 640 641 643 645 646 651 656
Discrete system      285
Dissipative system      170
DNN (delay neural network)      541
Dong      459
Double Hopf      593
Double zero singular point      609
Double-zero      593
Dual/adjoint space      663
Dynamical system      111 167 203 208Ч210 229 285 293 316 321 489 495 550 591 594 640 656
Ecological system      550 591
Efficient computation      614 622
Eigen      551
Electrical circuit      627 634 636 638 645
Energy function      163 164 167 487Ч490 493Ч495 497 530
Equi-asymptotic stability      28 29 33 106 119
Equi-asymptotically stable      24 27 28 30 106 126 127
Equi-asymptotically stable with respect to      108
Equi-attractive      22 24 27 28 30 108
Equi-attractive with respect to      109
Equi-bounded      177 180
Equi-dissipative system      186
Equi-Lagrange asymptotically stable      186
Equi-Lagrange stable      177 179Ч181
Equilibrium      147 164 218 391 489 497 502 506 516Ч522 524 525 527Ч532 534 550 551 553 554 571 575 576 584 585 587 592 593 603 605 606 622 626Ч629 631Ч633 636 638 651 658 659 662
Equilibrium, point      195 489 491 492 495 497 500 501 503 511 512 526 527 529 532 535 536 538Ч543 546 554Ч570 594 598 602 603 607 608 615 631 641 645 646
Equilibrium, solution      592
Error dynamics      459 460 466 468 469
Existence and uniqueness      2 215 489 535
Exponential estimation      189
Exponential rate      301
Exponential stability      24 27 29 33 83 86Ч89 106 127 173 175 188 197
Exponentially periodic      546
Exponentially stable      28 29 51 83 84 86Ч93 95 97Ч102 104 109 110 175 196 198 218 287 290 297 300 301 303 304 311Ч313 315 323 328 369
Exponentially stable with respect to      98 99 233
Exponentially stable, manifold      218
Extended center      601
Extensive energy function      495
Extreme stability      302
Extremely asymptotically attractive      303
Extremely asymptotically stable      303 304 309
Extremely attractive      302
Extremely exponentially stable      303 304
Extremely stable      302Ч304
Extremely uniformly attractive      303
Extremely uniformly stable      303
Family of circles      3
Family of level curves      6
Family of limit cycles      593 607 626 627 637
Family of periodic solutions      3
Family of spirals      138
Feedback, control      389 392 628 629 631 638 652 654 659 667 669
Feedback, controller      594 645 646 649 652
Feedback, gain      460
Feedback, loops      454
Feedback, system      62
Fine focus point      609
First comparison theorem      14
First standard form      410
Fixed point      593 605 609 640 646Ч652 654Ч657
Floquet Ч Lyapunov theory      95 96
Flutter, boundary      658 660 666 668
Flutter, instability      658 667 669
Flutter, instability, boundary      660
Flutter, speed      658 662 667 668
Flutter, stability boundary      668
Flutter, velocity      667 668
Focus value      593 594 597 599 601Ч603 606 607 611 612
Frequency characteristic curve      403 406
Frequency-domain approach      69
Frozen coefficient matrix      283
Frozen coefficient method      282 283
Functional differential equation      203 285
Functional equation      321
Fundamental matrix      210 213 214 217 473 483
Fundamental sequence      297 300
Fundamental solution matrix      36 77 78 96 286
Gauss Ч Seidel type iteration method      290 294
General neural network      443 550 564
Generalized Hopf bifurcation      599 630
Generalized separable variables      278
Gershgorin theorem      468 553
GershgorinТs circular disc theorem      50
Gilpin and Ayala model      551
GLNS (general linear neutral system)      378
Global (large) limit cycle      609
Global analysis      591
Global behavior      591
Global bifurcation      593
Global stability      241 271 502
Global time-delay independent stability      431
Globally asymptotic stability      29 33 82 106 379 468 509 515 523 535 553
Globally asymptotically stable      24 30 108 148 149 164 242 248Ч250 252 254 260Ч262 264 265 267 268 305 324 326 331 338 342 344 347Ч350 354 358 379Ч382 466 467 470 474 476Ч478 480 485 486 488Ч490 503Ч509 515Ч522 524 526 527 529 535 538Ч541 555Ч563
Globally asymptotically stable with respect to      271 278
Globally asymptotically time-delay independently sable      471
Globally asymptotically time-delay independently sable in the Hurwitz sector      471
Globally attractive      24 30 237
Globally attractive and positive invariant set      191 192 195
Globally attractive set      189 190 195 515 518
Globally equi-asymptotic stability      33
Globally equi-uniformly asymptotic stability      30
Globally exponential stability      24 30 33 457 502 512 515 530 566
Globally exponentially attractive      577 580
Globally exponentially attractive and positive invariant set      193
Globally exponentially attractive set      189 191 192 194 467 491Ч493 518
Globally exponentially Lagrange stability      189
Globally exponentially stable      127 128 245Ч248 328 329 355 502 505Ч507 511 512 514 515 532 534 541 543 546 566Ч571 575Ч577 580 581 583Ч585 587
Globally quasi-uniformly asymptotically stable      24 33
Globally stable      29 271 382 383 391 392 402 461
Globally stable with respect to      270 271 273Ч277 281Ч284
Globally uniformly, asymptotic stability      33 82 173
Globally uniformly, asymptotically stable      24 28 108 239
Globally uniformly, attractive      24 216
Globally uniformly, Lipschitz stable      203
Governing equation      659
Gradient method      163Ч165
Gramer law      60
Gronwall Ч Bellman inequality      14 86 232
Grossberg      499
Halanay      350
Hale      361 383
Henon map      646 651Ч657
Heteroclinic      591 593
hilbert      608
Hilbert number      608 609
HilbertТs 16th problem      608
Homeomorphic mapping      214 215
Homeomorphism      79 209 215
Homoclinic      591 593
Homogeneous      77 80
Homogeneous system      212
Hopf bifurcation      591Ч594 597 602 606 608 609 622 624Ч634 636Ч647 649Ч658 660Ч663 666 667 669
Hopf bifurcation, control      591 594 626 629 657 658 669
Hopf circle      640
Hopf singularity      597 609 614 615
Hopf type      611
Hopf-type critical point      599 660
Hopf-type singular point      599
Hopf-zero      535
Hopfield      487 488 491 493Ч498 530
Hopfield type energy function      489 490 493
Hopfield, energy function      489 493 495 499
Hopfield, network      490 495 515
Hopfield, neural network      491 493 497 498 502 515 522 564
Hopfield, stable      489
Hopfield-type stability      495 498
Hurwitz, angle      363 364 367 369Ч376 381 383 392 397 398 402Ч410 412 418 419
Hurwitz, condition      1
Hurwitz, criterion      38 636 642
Hurwitz, matrix      17 19 37 38 43 45Ч54 59 61Ч63 66 67 88Ч90 92 95 97Ч100 392Ч394 401 407 452 456 458 470 472 474 475 501 514 553 555 569
Hurwitz, polynomial      431
Hurwitz, sector      470 471 475 477Ч482 485
Hurwitz, stability      16
Hurwitz, stable      16 35 36 68 421 422 424 435 436 438 443 446 460 463Ч465
Image processing      563
Incipient instability      640 650
Indirect control system      358 384
Induction machine      603Ч605 607
Infimum      14
Infinite interval Lorenz system      192Ч194
Infinitesimal deformation      555
Infinitesimal upper bound      5 6 117 119 123Ч125 131Ч133 136 144 153 173 174 176 225 325 326 338 339
Integral inequality      13 376
Interval matrix      315 316 318 319
Interval matrix, stability      450
Intrinsic harmonic balancing technique      591
Invariant circle      641
Invariant set      494 525 526 550
Invertible transformation      241
IoossТs Hopf bifurcation theory      643
Isogeny sign transform      18 19
Isolated fixed point      550
Isolated subsystems      209Ч211 217 218 286 289 290 310 314 316 318 366 373
Iteration method      285 290 302 305 309 310 315
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