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Lynch S. — Dynamical Systems with Applications Using Mathematica®
Lynch S. — Dynamical Systems with Applications Using Mathematica®



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Название: Dynamical Systems with Applications Using Mathematica®

Автор: Lynch S.

Аннотация:

Dynamical Systems with Applications Using Mathematica® provides an introduction to the theory of dynamical systems with the aid of the Mathematica computer algebra package. The book has a very hands-on approach and takes the reader from basic theory to recently published research material. Emphasized throughout are numerous applications to biology, chemical kinetics, economics, electronics, epidemiology, nonlinear optics, mechanics, population dynamics, and neural networks.

Throughout the book, the author has focused on breadth of coverage rather than fine detail, with theorems and proofs being kept to a minimum. The first part of the book deals with continuous systems using ordinary differential equations, while the second part is devoted to the study of discrete dynamical systems. Exercises are included at the end of every chapter. Both textbooks and research papers are presented in the list of references.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2007

Количество страниц: 448

Добавлена в каталог: 10.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Fractal, structure      156 160 294
Fragmentation ratios      346
Function      4
Function, approximators      393
Fundamental memory      402
Fuzzy discs      348
Gauss — Newton method      395
Gaussian, input pulse      322
Gaussian, map      281
Gaussian, pulse      446
Gauss’ law, electricity      307
Gauss’ law, magnetism      307
Generalized delta rule      395
Generalized fractal dimension      346
Generalized fractal dimensions      345
Generalized mixed Rayleigh — Lienard equations      213
Generalized synchronization      378
Global bifurcation      209 219
Globally asymptotically stable      154 167
Glucose in blood      37
Gradient      42
Gradient, vector      395
Graphic      91
Graphical method      264 319
Green’s Theorem      92
Grey scale      354
Grobner bases      201
Gross national product (GNP)      286
Hamiltonian      112 425
Hamiltonian, systems with two degrees of freedom      178
Handcrafted patterns      408
Hard bifurcation      138
Hartman’s theorem      54
Harvesting      80 141
Harvesting, policy      251
Hausdorff dimension      345
Hausdorff index      338
Hausdorff — Besicovich dimension      347
Heaviside function      390
Hebb’s, learning law      391
Hebb’s, postulate of learning      403
Help pages      2
Henon map      282 341 348 423 426
Henon — Heiles Hamiltonian      179
Henry      30
Heteroclinic bifurcation      189
Heteroclinic orbit      91 116 189 220
Heteroclinic tangle      189
Heterogeneous      343
Hidden layer      392 396
Hilbert numbers      218
history      139
Hodgkin — Huxley equations      87
Holling — Tanner model      74 107 128
Homoclinic bifurcation      159 189 209
Homoclinic loop      209 214
Homoclinic orbit      116 189 220
Homoclinic tangle      189
Homogeneous      343
Homogeneous, differential equation      23
Hopf bifurcation      133 142
Hopf singularity      142
Hopfield, model, continuous      399
Hopfield, model, discrete      402
Hopfield, network      121 398 416 424 426
Hopfield, neural network      393
Horseshoe dynamics      189
Host–parasite system      78
Human population      61 256
Hyperbolic attracting      229
Hyperbolic critical point      54
Hyperbolic fixed point      175 284
Hyperbolic iterated function system      337
Hyperbolic repelling      229
Hyperbolic stable limit cycle      175
Hyperbolic unstable limit cycle      175
Hysteresis      139 283 324
Ideal      201
if      10
Ikeda map      287 315 327 382
Image, analysis      349
Image, compression      332
import      411
incident      309
INDEX      95
Inductance      30
Infected population      78
Infectives      61
Inflation unemployment model      291
Information dimension      346
Inhibitory      389
Initial value problem (IVP)      20
Input vector      389
Insect population      82 258
Instability      322
Instant physician      393
Integrable      178
Integrate and fire neuron      87 389
Integrating factor      24
Intensity      313
Interacting species      69 434
Intermittency      162 168 278
Intermittency, route to chaos      279
InterpolatingFunction      165
Invariant      90 160 316
Invariant, axes      58 72
Inverted Koch, snowflake      423
Inverted Koch, square      336
Isoclines      42
Isolated periodic solution      86
Isothermal chemical reaction      61
Iterated function system (IFS)      337
Iteration      242
Jacobian      134
Jacobian, matrix      54 152 164 284 372
Jordan curve      92 232
jth point of period i      270
Julia set      294 297 332 426
KAM, theorem      181
KAM, tori      181
Kernel machines      393
Kerr, effect      309 314
Kerr, type      314
kinetic energy      112
Kirchhoff’s current law      30
Kirchhoff’s laws      399
Kirchhoff’s voltage law      30
Koch, curve      333
Koch, snowflake      357
Koch, square      334
Ladybirds and aphids      72
Laminarize      366
Landolt clock      162
Laplace transform      31
Large-amplitude limit cycle      138
Large-amplitude limit cycle, bifurcation      138
Laser      142 287 310 366
Law of mass action      61
Learning, ate      395
Learning, process      388
Least mean squared (LMS) algorithm      391
Legendre transformation      347
Leslie, matrix      248
Leslie, model      247
Lexicographical order      202
Lie detector      394
Lienard equation      198
Lienard plane      227
Lienard system      88 94 107 208 227
Lienard system, large parameter      231
Lienard system, local results      235
Lienard theorem      237
Limit cycle      79 86 90 165 425
Limit cycle, hyperbolic      207
Limit cycle, neuron      88
Limit cycle, nonexistence      422
Limit cycle, three-dimensional      154
Lindstedt — Poincare technique      100
Linear differential equation      24
Linear phase shift      314 325
Linear stability analysis      34 318
Linear transformation      147
Linearization      54
Linearized system      54
Lipschitz condition      32
Lipschitz continuous      32
listdensityplot      300
listplot      189
Local bifurcation      219
Logic gates      308
Logistic equation      20
Logistic growth      75
Logistic map      273 368 426
log–log plot      343
Lorenz attractor      160
Lorenz equations      158 366
Loss in the fiber      313
Lotka — Volterra model      72 128 168
Low-gain saturation function      390
Lowest common multiple      204
Lyapunov domain of stability      121
Lyapunov exponent      156 279 426
Lyapunov function      117 119 153 196 229 415 422
Lyapunov function, Hopfield network      399
Lyapunov quantities      235
Lyapunov quantity      197
Lyapunov stability      398
Lyapunov stability theorem      118
Lynx and snowshoe hares      72
Magnetic field vector      306
Magnetic flux      306
Magnetostrictive ribbon      366
Mandelbrot      340
Mandelbrot, set      296 298 332
Manifold      46
Manipulate      4 8 140
MAP      288
Mathematica-based exam      424
Maximal interval of existence      32 38 89
Maxwell — Bloch equations      308
Maxwell — Debye equations      308
Maxwell’s equations      306
McCulloch — Pitts neuron      391
Mean, infectivity period      168
Mean, latency period      168
Mechanical oscillator      66
Mechanical system      89 139
Melnikov function      207
Melnikov integral      207
memory devices      308
Meteorology      158
Method of multiple scales      103
Method of steepest descent      394
Microparasite–zooplankton–fish system      78
Minimal chaotic neuromodule      409
Minimal Grobner basis      205
Mixed fundamental memories      404
Mixing      266
MODULO      203
Monomial      201
Monomial, ordering      202
Mortgage assessment      393
Motif      332
Multidegree      203
Multifractal      343
Multifractal, formalism      343
Multifractal, Henon map      354
Multifractal, Sierpinski triangle      354
Multifractal, spectra      345
Multistable      117 137 138 165 194 410
Murder      37
Mutual exclusion      70
National income      246
NDSolve      35 64
Negative limit set      90
Negative semiorbit      89
Negatively invariant      90
NestList      288
Net reproduction rate      253
Network architecture      389
Neural network      287 376 388
Neurodynamics      408
Neuromodule      408
neuron      87 388 416
Neuron, module      287
Neuronal model      389
Newton’s Law of Cooling      37
Newton’s law of motion      112
Newton’s method      395
Noise      368
NOLM      306
NOLM with feedback      312
Nonautonomous system      87 181
Nonconvex closed curve      96
Nondegenerate critical point      113 196
Nondeterministic chaos      154 364
Nondeterministic system      388
Nonexistence of limit cycles      95
Nonhyperbolic critical point      54 117 421
Nonhyperbolic fixed point      284
Nonintegrable      178
Nonlinear center      197
Nonlinear optics      287
Nonlinear phase shift      314
Nonlinear refractive index coefficient      314
Nonlinearity      139 308
Nonperiodic behavior      156
Nonsimple canonical system      43
Normal form      128 134
Normalized eigenvector      254
Not robust      74
Notebook      2
Occasional proportional feedback (OPF)      365
ODE      18
Ohm      29
Ohm’s Law      29
Optical bistability      308
Optical computer      308
optical fiber      310
Optical fiber double ring      312
Optical memories      308
Optical resonator      140
Optimal sustainable      253
Orbit      42 89
Oscillation of a violin string      86
Output vector      389
Ozone production      167
Palette      2
ParametricPlot      64
Partial differential equation      18
Partition      288
Partition function      345
Pascal’s triangle      358
Passive circuit      32
Peixoto’s theorem in the plane      128
Pendulum      112 123 183 193
Perceptron      391
Period      207
Period, bubblings      281
Period, doubling      162
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