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Sun J.Q. (Ed), Luo A.C. (Ed) — Bifurcation and Chaos in Complex Systems
Sun J.Q. (Ed), Luo A.C. (Ed) — Bifurcation and Chaos in Complex Systems



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Название: Bifurcation and Chaos in Complex Systems

Авторы: Sun J.Q. (Ed), Luo A.C. (Ed)

Аннотация:

The book presents the recent achievements on bifurcation studies of nonlinear dynamical systems. The contributing authors of the book are all distinguished researchers in this interesting subject area. The first two chapters deal with the fundamental theoretical issues of bifurcation analysis in smooth and non-smooth dynamical systems. The cell mapping methods are presented for global bifurcations in stochastic and deterministic, nonlinear dynamical systems in the third chapter. The fourth chapter studies bifurcations and chaos in time-varying, parametrically excited nonlinear dynamical systems. The fifth chapter presents bifurcation analyses of modal interactions in distributed, nonlinear, dynamical systems of circular thin von Karman plates. The theories, methods and results presented in this book are of great interest to scientists and engineers in a wide range of disciplines. This book can be adopted as references for mathematicians, scientists, engineers and graduate students conducting research in nonlinear dynamical systems.

* New Views for Difficult Problems
* Novel Ideas and Concepts
* Hilbert's 16th Problem
* Normal Forms in Polynomial Hamiltonian Systems
* Grazing Flow in Non-smooth Dynamical Systems
* Stochastic and Fuzzy Nonlinear Dynamical Systems
* Fuzzy Bifurcation
* Parametrical, Nonlinear Systems
* Mode Interactions in nonlinear dynamical systems


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2006

Количество страниц: 388

Добавлена в каталог: 23.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$Z_q$-equivariance      52
$Z_q$-equivariant, Hamiltonian vector field      51 52
$Z_q$-equivariant, planar vector field      50
$Z_{10}$-equivariant planar vector field      54
Abed, E.G.      79—81 124 259 275
Abed, E.H.      24 121 335 335
Abraham, R.H.      198 274
Accessible subdomain      129 187
Active queue management schemes      24
Additive fuzzy noise      245
Aracil, J.      230 275
Arnold, L.      214 274
Arnold, V.I.      2 121 284 288 294 335
Arrowsmith, D.K.      284 285 312 313 335
Asmis, K.G.      317 338
Asymptotic stability      287
Attractor invariant      255
Backward, algorithm      234
Backward, search algorithm      234
Badian, J.      340 376
Bajaj.A.K.      281 338
Balachandran, B.      259 277 284 288 337
Bapat.C.N.      128 159
Bautin, N.N.      38 41 121
Baxendale, P.      2l4 274
Bellman, R.      283 335
Berns, D.      37 127
Bernussou, J.      284 335
Bessel functions of the first kind      344
Bi, Q.      3. 97 99 125
Bibb, J S.      285 290 338
Bifurcation of fuzzy nonlinear oscillators      240
Bifurcation of limit cycles      5 53 307
Bifurcation of nonlinear systems with small random disturbances      212
Bifurcation of one-dimensional fuzzy systems      235
Bifurcation, analysis      14
Bifurcation, control      73
Birkhoff, G.D.      127 189 284 335
Bleich, M.E.      24 121
Bliiel.R      205 277
Blows, T.R.      41 123
Bogoliubov, N.N.      283 336
Bolotin, V.V.      280 336
Brambilla, M.      212 274
Brandt, M.E.      24 121
Broucke, M.      128 189
Budd, C.J.      128 189
Bunin, A.      74 123
Bursal, F.H.      260 274
Butcher, E.A.      287 297 336 337
Carroll, T.L.      73 124
Caughey, T.K.      127 128 190 214 274
Cell mapping method      193 231
Center manifold, reduction      7 11 12 292
Center manifold, theory      38 294
Chajes, M.      259 274
Champney, A.R.      128 189
Chan, H.S.Y.      50 53 123
Chaos, control      73
Chaos, synchronization      73 74
Chaotic attractors      202
Chaotic boundary crisis      200
Chaotic crisis      198
Chaotic saddle      202
Chebyshev polynomial expansion      290 297
Chen, G.R.      2 4 24—30 32 37 73 75—80 121—125 259 274
Chen, H.B.      44 46 47 122
Chen, L.D.      129 156 190
Chen, R.C.      335 335
Chen, Y.Y.      193 274
Chen, Z.      25 122
Cheng, A.      259 274
Chiang, W.L.      212 214 274 275
Chin, C.M.      37 124
Chin, H.M.      193 215 221 274 276
Choi, H.T.      193 275
Chow, S.-N.      285 296 312 336
Chua system, simple      105
Chua system, smooth      105
Chua, L.O.      105 122
Chung, K.L.      197 274
Chung, K.W.      50 53 721
Circular plate      339 341
Clairaut, A.      282 336
Closed set      197
Coalson, R.D.      281 336
Codimension, one bifurcations      301
Codimension, two bifurcations      245
Comer, D.J.      193 277
Commutative systems      297 313
Competitive mode      92—94
Complex center      46
Connect able domain      129
Corless, R.      40 125
Corner points or vertex      133
Crasemann, B.      281 337
Crauel, H.      214 275
Crespo, L.G.      193 258 260 261 275
Crises in deterministic systems      198
Crutchfield, J.P.      214 215 217 275
Cuesta, F.      230 275
Cuomo. KM.      73 122
Cyclic fold bifurcation      288 307 309
Cyclic group      50
Danby, J.M.A.      281 336
Das, D.      230 277
David, A.      286 318 321 324—326 330—332 335 336 337
Davis, S.H.      281 337
Davison, M.      5 92 125
Deb, S      25 122
Delay differential equations      24
Den Hartog, J.R      128 159
Deng, W.      128 189
Detuning parameters      352 361
di Bernardo, M.      128 189
Discontinuous dynamic system      131
Disjoint      132
Doedel, E.      357 376
Doi, S.      230 275
Domain accessibility      129
Domains of attraction      195
Dong, W.M.      212 214 274 275
Dong, X.      2 4 73 122
Douay, A.C.      258 275
Double crises      210 211
Double inverted pendulum      327
Dufling — Van der Pol oscillator      245
Dulling oscillator      357
Dulling oscillator with small random excitations      220
Edwards. D.      193 275
Efstathiades, G.J.      341 376
Endo.T.      258 277
Equilibrium      7
Equilibrium, cell      194
Essex, C      5 37 92 113 124 125
Evan-Ivanowski, R.M.      280 336
Extended center      46
External mode      93
External mode, resonance      352
Fang, T.      194 226—229 278
Farmer, J.D.      214 215 217 275
Farooq, A.      280 336
Feigenbaum, M.J.      215 275
Ferraris, G.      280 337
Field, R.J.      104 122
Fillippov, A.F.      128 132 /S9
Flandoli, F      214 275
Flashner.H.      284 336
Flip      288
Flip, bifurcation      301 313
Floquet multipliers      288
Floquet multipliers, theory      281 282 289
Floquet multipliers, transition matrix      288 298
Floquet — Lyapunov theory      74
Floquet, G.      281 287 336
Flowers, G.T.      280 338
Foale, S      193 275
Formal monomial form      294
Friction-induced oscillator      158
Friedman, Y.      232 275
Friedmann, P.P.      280 336
Fu, J.H.      24 121 335 335
Fundamental solution      282
Fuzzy, attractor      241 255
Fuzzy, attractor, chaotic      242
Fuzzy, bifurcation      230 239 242
Fuzzy, dynamical system      231
Fuzzy, generalized cell mapping      231
Fuzzy, generalized cell mapping, system      232
Fuzzy, nonlinear dynamical systems      233
Fuzzy, set      231 237
G-equivariant vector field      50
G-invariant function      50
Gallas, J.A.C      211 275
Gaussian white noise      221
Gegg, B.C      129 158 161 163 164 186 190
General control database      260
General resonance condition      303
Generalized cell mapping      193 195
Genesio, R.      259 275
Ghosh, A.K.      341
Glass, L.      281 336
Global Lipschitz condition      74
Global ultimate boundedness of chaotic systems      74
Goldberger, A.L.      281 337
Gong, PL.      241 275
Gorman, M.      281 338
Grassia, P.G.      281 336
Grazing flow      141 143
Grazing flow of the first kind      150
Grazing flow of the second kind      150
Grazing flow of the third kind      150
Grebogi, C.      4 73 124 198 202 205 211 242 259 275 277 278
Griffith, J.S.      262 276
Gua, S.M.      73 122
Guckenheimer, J.      2—4 7 82 122 192 245 276
Guder, R.      193 276
Guevara, MR.      281 336
Gultalu.R.S.      284 336
Gupta, P.B.D.      230 277
Hackl, K.      259 274
Hagood, N.W.      258 275
Haken, H.      92 122
Hale, J.      12 122 288 336
Hale, J.K.      192 276
Han, M.      38 39 42 48 122 125
Han, R.P.S.      127 128 189 190
Harb, A.M.      37 124
Hardy, Y.      103 122
Hassard, B D.      2 24 30 122
Hawthorne, E.I.      281 336
He, Q.      194 226—229 275
Hilbert, D.      38 57 122
Hilbert’s 16th problem      6 38
Hill, G.W.      281 336
Hill’s method      281
Hirschfelder, J.O.      281 336
Holmes, PJ.      2—4 7 82 122 128 190 192 245 276
Homoclinic and heteroclinic bifurcation      4 61
Homoclinic and heteroclinic bifurcation, values      61
Homological equation      295
Homsy, G.M.      280 281 336
Hong, L.      194 211 241 276
Hopf bifurcation      2 4 6 7 10 15 26
Hopf bifurcation, control      28 77
Hopf bifurcation, controling      79
Hopf bifurcation, double      7
Hopf bifurcation, onset of      30
Hopf bifurcation, parameters      59
Hopf bifurcation, secondary      288 309 327
Hopf bifurcation, subcritical      268
Hopf, E.      4 122
Hopf-type critical point      39
Hou, L.      128 190
Hrinca, I.      258 276
Hsu, C.S.      193 194 196 215 217 221 226 231—236 260 274 276 278 280 284 336
Huang, Q.      50 53 123
Huang, W.T.      44 46 123
Huberman, B.A.      214 215 217 275
Hunt, B.      259 277
Hyperbolic flow      153
Ibrahim, R.A.      214 276
Inaccessible subdomain      129 187
Indeterminate crisis      202
Inoue, J.      230 275
Instability flutter      15
Interior crisis      200
Internal mode      93
Internal resonance      340 361
Internal resonance, condition      352
Iooss, G.      288 336
James, E.M.      47 122
Jiang, J.      193 276
Jin, J.-D.      327 337
Johari, R.      25 122
Johnson, W.      280 337
Joseph. D.D.      288 336
Jump phenomenon of resonance      307
Juneja, V.      283 335
Kalenge.M.C.      41 123
Kan, I.      205 277
Kapitaniak, T.      214 276
Kazarinoff, N.D.      2 24 30 122
Kelly, F.P      24 25 122
Kennedy, J.      205 276
Kim, C.H.      340 376
Kim, M.C.      193 276
Kleczka.M      128 189
Knuth.D.E.      215 276
Kobs, T.      258 276
Kocak, H.      192 276 288 336
Koksch, N.      74 123
Komuro.M.      105 122
Kostelich, E.      259 277
Kotulski.Z.      214 276
Kowalczyk, K.      128 149
Krauskopf, B.      24 124
Kreuzer, E.      128 189 193 276
Krousgrill, CM.      281 338
kth-order singular point      46
Kukles, I.S.      38 122
Kumagai, S.      230 275
Kunze, M.      128 189
Lagrange. J.-L.      282 337
Lai, Y.C.      198 205 277
Lalanne, M.      280 337
Lee, W.K.      340 341 376
Leine, R.I.      128 189
Leissa, A.W.      341 351 376
Leonov, GA.      74—76 123
Lever, P.J.A.      260 275
Lewis, F.L.      260 277
Li, C.F.      50 53 123
Li, C.G.      24—27 29 30 32 123
Li, Ch.      285 296 312 336
Li, D.      75 76 123
Li, J.      38 46 50 123 124
Li, J.B.      38 50—53 56 123
Liao, X.      74 125
Liao, X.F.      24—27 29 30 32 123
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