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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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345 151 48 146 151 48 146 151 345 151 55 150 55 150 345 345 Absorptive nonlinearity 309 Action potential 87 Activation function 389 415 Activation level 399 Activation potential 390 ADALINE network 391 Affine linear transformation 337 Age class 80 247 Algebraicity of limit cycles 228 Ampere 29 Ampere’s Law 307 Anemia 285 Angular frequency of the wave 308 animate 437 Ants and termites 70 Aperiodic 160 273 Aperiodic behavior 156 Applying a damper 365 Arrhythmic 366 Artificial Intelligence Group 394 Artificial Neural Networks 388 Associative memory 392 398 Asymptotic expansion 98 Asymptotically stable critical point 117 Asynchronous updating 403 Attractor 156 Attributes 396 Autocatalysis 163 Autonomous differential equation 32 Autonomous system 146 Auxiliary system 378 Auxiliary system approach 378 Average Lyapunov exponent 280 Axial flow compressors 138 Axon, 389 Axon, algorithm 396 Axon, backpropagation 394 Backward training 296 Bandwidth 308 Barnsley’s fern 338 Basin of attraction 124 156 284 296 Basis 202 Batch data 398 Belousov — Zhabotinski reaction 162 168 Bendixson’s criteria 95 Bias 389 Bifurcating limit cycles from a center 207 Bifurcation at infinity 219 Bifurcation, curve 130 Bifurcation, diagram 130 Bifurcation, diagram, CR resonator 311 Bifurcation, diagram, Duffing equation 187 Bifurcation, diagram, Gaussian map 283 Bifurcation, diagram, logistic map 278 Bifurcation, diagram, neuromodule 411 Bifurcation, diagram, SFR resonator 322 Bifurcation, point 275 Bifurcation, value 128 biology 285 Bipolar activation function 390 Bistability 137 139 281 322 408 Bistable 139 165 282 309 Bistable, cycle 162 Bistable, device 308 323 Bistable, neuromodule 410 Bistable, optical resonator 366 Bistable, region 188 193 311 316 411 Bistable, solution 139 Blowflies 274 Bluegill sunfish 78 Boston housing data 396 Boundaries of periodic orbits 298 Box-Counting Dimension 340 345 Brain functions 388 Butterfly effect 159 Button 2 Canonical form 42 43 146 Cantor, multifractal 350 Cantor, set 189 332 Capacitance 30 Cardioid 299 Cardiology 363 Carrying capacity 21 Cavity, ring (CR) resonator 309 Cavity, round-trip time 310 Center 45 113 196 Center, manifold 151 Center, manifold, theorem 151 Changing the system parameters 365 Chaologist 364 Chaos 154 264 266 311 Chaos, control 408 417 Chaos, control, OGY method 365 367 Chaos, control, periodic proportional pulses 382 Chaos, game 336 Chaos, synchronization 376 Chaotic attractor 156 184 317 Chaotic attractor, Henon map 372 Chaotic attractor, neuromodule 409 Chaotic attractor, Sierpin?ski 337 Chaotic dynamics 158 Chaotic phenomena 262 Chapman cycle 167 Characteristic equation 244 Characteristic exponent 228 Characteristic multiplier 175 Charge density 307 Chemical kinetics 25 61 89 162 376 Chemical law of mass action 25 Chemical reaction 37 Chemical signals 389 Chemical substance 38 Chua’s circuit 89 160 365 383 Circle map 176 Circular frequency of light 310 Classical symmetry argument 198 Classification of critical points 48 Clipping problem 348 Clockwise, bistable cycle 440 Clockwise, hysteresis 311 Clockwise, hysteresis, loop 193 Cluster 392 Coarse Holder exponent 347 Codimension 1 bifurcation 142 Codimension 2 bifurcation 142 coexistence 70 Coexisting chaotic attractors 284 col 44 ColorFunction 297 Commutative ring 201 Competing species 69 82 108 compile 288 300 Complete synchronization 376 Completely integrable 178 Completely reduced 203 COMPLEX 300 Complex, eigenvalues 44 244 Complex, iterative equation 318 Compound interest 242 Computer algebra 201 Concentration 25 Conditional Lyapunov exponents 377 Conductivity 307 Conformal mapping 294 Conservation of energy 112 Conservation of mass 62 Conservative 112 Contact rate 168 Content-addressable memory 399 Control, curves 370 Control, engineering 393 Control, parameter 367 Control, region 367 Controlling chaos, Henon map 372 Controlling chaos, logistic map 368 Conversational agents 394 Convex closed curve 94 Convoluted surfaces 150 Core area of the fiber 314 Corollary to Poincare — Bendixson theorem 91 Correlation dimension 346 Coulomb 29 Coulomb’s law 30 Counterclockwise hysteresis 311 Coupler 313 Critical point 34 48 146 150 Critical point at infinity 222 Culling 80 Culling, policy 251 Current 29 Current, density 307 Cusp 61 Cylindrical polar coordinates 152 Damping 88 Damping coefficient 227 Dangerous bifurcation 138 Daphnia dentifera 78 Data Mining 388 databases 396 Defibrillator 366 Degenerate, critical point 113 Degenerate, node 46 Degree 218 Degree, lexicographical order 202 Deleted neighborhood 92 Delta learning rule 391 394 Demonstrations Project 9 Dendrites 389 Derivative of the Poincare map test 175 Desired vector 394 Deterministic 154 Deterministic chaos 154 364 Deterministic system 388 df 338 Dielectric 308 Difference equation 242 416 Differential amplifier 308 Diffusion limited aggregates (DLA) 350 DIMENSION 345 dimensions 411 Direction, field 42 Direction, vector 42 Dispersive nonlinearity 309 Displacement function 197 DisplayFunction 64 Distributive laws 201 Divergence test 197 DO 9 Domain of stability 71 156 296 Double coupler fiber ring resonator 311 328 Double scroll attractor 162 Double well potential 117 Driver system 376 378 Drop 288 DSOLVE 35 Duffing equation 98 183 Duffing system 365 425 Dulac’s criteria 92 Dulac’s theorem 218 Economics 67 286 291 376 Economics, model 246 Eigenvector 46 Electric circuit 29 66 89 160 399 Electric displacement 307 Electric displacement, vector 307 electric field 313 318 366 Electric field, strength 306 Electric flux density 307 electromotive force (EMF) 30 Elliptic integral 208 Energy level 180 Enrichment of prey 80 Environmental effects 80 Epidemic 38 60 80 88 168 Epoch 392 Equilibrium point 34 Ergodicity 279 367 Error, backpropagation rule 396 Error, function 394 Erythrocytes 285 Euclidean dimension 345 Exact 21 Exact differential equation 21 Examination-type questions 421 Excitatory 389 Existence and uniqueness limit cycle 89 Existence, theorem 32 Extinct 70 Fabry — Perot interferometer 309 Fabry — Perot resonator 309 Farad 30 Faraday’s law 30 Faraday’s law of induction 306 Feedback 139 308 321 Feedback, mechanism 410 Feedforward single-layer network 391 Feigenbaum constant 279 Fiber parameters 325 Fibonacci sequence 9 256 Field 201 Fine focus 196 First integral 112 First iterative method 320 324 417 First return map 172 First-order difference equation 242 Fish population 20 141 258 Fitzhugh — Nagumo equations 87 Fitzhugh — Nagumo oscillator 87 Fixed point 34 266 Fixed point, period, m 176 Fixed point, period, N 271 Fixed point, period, one 172 315 369 Fixed point, period, two 369 Fixed point, size box-counting algorithm 348 Fixed point, weight box-counting algorithm 348 Flatten 189 Flow 89 Focal values 197 Fold bifurcation 142 Forced system 181 Forward rate constant 26 Fossil dating 36 Fractal 332 339 Fractal, attractor 156 338 Fractal, Cantor set 339 Fractal, dimension 338 Fractal, geometry 332 Fractal, Koch, curve 339 Fractal, Koch, square 339 Fractal, Sierpinski triangle 340
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