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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
Period, doubling, bifurcations to chaos      278
Period, limit cycle      77 90 164
Period, undoubling      187 281
Period-one behavior      263
Period-one cycle      154
Period-three behavior      264
Period-two behavior      155 263
Periodic behavior      86
Periodic orbit      207
Periodic windows      278
periodicity      262 266
Permittivity of free space      307
Perturbation methods      98
Phase portrait      42
Phase shift      313
Physiology      376
Piecewise linear function      390
Pitchfork bifurcation      131
pixels      348
Planar manifold      147
Plastics      349
PlotJoined      356
PlotStyle      80
PlotVectorField      64
Poincare — Bendixson theorem      91 181 226 232
Poincare, compactification      220
Poincare, map      90 158 172 208 283 367
Poincare, section      172 425
Poisson brackets      178
Polar coordinates      45 221
Pole placement technique      367
Pollution      80
Polymer      349
Population      67
Population of rabbits      62
Positive limit set      89
Positive semiorbit      89
Positively invariant      90
Potato man      300
Potential difference      29
potential energy      112 117
Potential function      117
Power      313
Power of a waterwheel      67
Power, law      341
Power, spectra      162
Power, splitting ratio      313
Prandtl number      159
Predation      78
Predation, rate      75
Predator–prey      88
Predator–prey, models      72
Predator–prey, system      82
Prepend      288
Probe vector      403
Propagation      313
Psychological profiling      394
Pyragas’ method      365
qth moment      345
Qualitative behavior      42
Qualitatively equivalent      49
Quasiperiodic      179 411 417
Quasiperiodic forcing      183
Quasiperiodic route to chaos      162
Quasiperiodicity      178
Radioactive decay      424
Random behavior      154
Random[ ]      356
Random[Integer]      300
Rate, constant      26
Rate-determining steps      26
Rationally independent      177
Rayleigh number      159
Rayleigh system      86
Reaction rate equation      26
Real distinct eigenvalues      43
Recurrence relation      242
Recurrent neural network      392 398
Red and grey squirrels      70
Red blood cells      285
Reduced      203
Reduced, Grobner basis      205
Reflected      309
Refractive index      309
Refractive nonlinearity      309
Refuge      80
Regulator poles      367
Relative permeabilities      307
Relative permittivities      307
Repeated real eigenvalues      45
Resistance      29
Resonance terms      137
Resonant      136
Response system      376 378
Restoring coefficient      227
Restoring force      88
Restrictions in programming      236
Return map      197 422
Reverse rate constant      26
Reversed fundamental memories      404
Ring      201
Ringing      193
RLC circuit      32 88 183
Robust      77
Rossler, attractor      154
Rossler, system      154
Rubbers      349
S-polynomial      204
Saddle point      44 113
Saddle-node bifurcation      128
Safe bifurcation      137
Scaling      341 343
Sea lions and penguins      70
Seasonal effects      80
Seasonality      168
Second iterative method      320 324 417
Second part of Hilbert’s sixteenth problem      218
Second-order linear difference equation      243
Second-order ODE      31
Secular term      100
Sedimentary rocks      350
SeedRandom      411
Self-similar      332 345
Self-similar fractal      338
Semistable critical point      35
Semistable limit cycle      90 175 231
Sensitivity to initial conditions      156 262 266 364
Separable differential equation      18
Separation of variables      18
Separatrix      116
Separatrix, cycle      210
SFR      305
SFR, resonator      310 312
Sharks and fish      72
Show      64
Sierpinski triangle      336
Sigmoid function      390
Signal processing      350
Simple canonical system      43
Simple nonlinear pendulum      112
Simply connected domain      95
Singlet      167
Singular node      45
Slot      288
Smale horseshoe map      189 285
Smale — Birkhoff theorem      189
Small perturbation      34 318
Small-amplitude limit cycle      196
Soft bifurcation      137
Solar system      364
Solution curves      19
Solve      206
Soma      389
Spatial vector      306
speed of light      308
Spin-glass states      404
spirals      268
Spurious steady state      404
Stability      117 150
Stability, diagram      321
Stable critical point      34 117
Stable fixed point      275 295
Stable focus      45
Stable limit cycle      77 90
Stable manifold      46 48 55 146 150 367
Stable node      44
Staircases      268
Stationary point      34
Steady state      31 77
Stiff system      28 167
Stiffness      88
Stochastic methods      388
Stock market analysis      350
Stoichiometric equations      26
Stokes’ Theorem      307
Strange Attractor      156
Stretching and folding      262
Strictly dominant      249
Structurally stable      77 128
Structurally unstable      74 128
Subcritical Hopf bifurcation      137 159
Subharmonic oscillations      184
Summing junction      389
Supercritical Hopf bifurcation      137
Supervised learning      392
Susceptible population      78
Susceptibles      61
Sustainable      251
switches      308
Synaptic weights      388
Synchronization      365 376 408
Synchronization of chaos      376
Synchronous updating      404
Target vector      392 394
targeting      368
Taylor series expansion      34 54 284 318
Tent map      262 423
Three-dimensional system      146
Threshold value      61
Time series      79 277
Time series, chaos detection      157
Time series, plot      157
TodaHamiltonian      193
Topological dimension      345
Topologically equivalent      49
Torus      184
Total degree      201
Totally connected      296
Totally disconnected      296
Trajectory      42 89
Transcritical bifurcation      130
Transfer function      389 416
Transient      31
Transmitted      309
Transversal      197
Transversely      172
Traveling salesman problem      398
Triangular pulse      321
Trivial fixed point      270
Turbulence      349 364
Two-neuron module      400
Unconstrained optimization problem      394
Uncoupled      146
Uniform, asymptotic expansion      98
Uniform, harvesting      254
union      288
Unipolar activation function      390
Uniqueness threorem      32
Universality      279
UNIX      1 2
Unstable critical point      34 118
Unstable fixed point      275 296
Unstable focus      45
Unstable limit cycle      90
Unstable manifold      46 48 55 146 150
Unstable node      44
Unsupervised learning      392
VACUUM      307
Value of homes in Boston      396
van der Pol equation      98
van der Pol system      86 208
Vector field      42
Vector field, plot      401
Velocity of light      314
Verhulst’s equation      20 70
viscosity      159
Viscous fingering      332
Volt      29
Voltage drop      29
Wave equations      306
Wave vector      308
Wavelength      308
Wavelength, light      314
Windows      1
Wing rock      138
X-ray spectroscopy      349
XOR gate      391
Youngest class harvesting      253
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