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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.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2007Количество страниц: 448Добавлена в каталог: 10.05.2008Операции: Положить на полку |
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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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