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Mullin T. — The nature of chaos
Mullin T. — The nature of chaos



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Íàçâàíèå: The nature of chaos

Àâòîð: Mullin T.

Àííîòàöèÿ:

The Nature of Chaos reflects the interdisciplinary character and captures the excitement of this fast-moving area of science. Focusing on the uses and application of the latest ideas from dynamical systems theory, the topics covered range from physics to biology, with individual chapters on applications to chemistry, the weather, quantum mechanics, and engineering.


ßçûê: en

Ðóáðèêà: Ôèçèêà/Íåëèíåéíàÿ äèíàìèêà, Õàîñ/

Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö

ed2k: ed2k stats

Ãîä èçäàíèÿ: 1993

Êîëè÷åñòâî ñòðàíèö: 314

Äîáàâëåíà â êàòàëîã: 22.09.2005

Îïåðàöèè: Ïîëîæèòü íà ïîëêó | Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
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Ïðåäìåòíûé óêàçàòåëü
A/D converter      24
Accessible orbit      211
Arnol'd cat maps      299—300
Attraction, basin of      202—204
Attractor      xi—xii
Attractor, Lorenz      222—223
Attractor, reconstruction of      xii—xvi 27—34
Attractor, strange      xi 19
Attractor, Vallis      246
Attractor, weather      226
Australian blowflies      186
Autocorrelation function      26—27
Baroclinic waves      256
Basin erosion      214
Basin of attraction      xii 202—204
Benjamin      82
Berry's semiclassical theory      293—299 305
Bifurcation      11—13
Bifurcation diagram      12 137
Bifurcation, chaotic saddle      213
Bifurcation, codimension-1      56—57
Bifurcation, codimension-2      58 206
Bifurcation, flip      204
Bifurcation, fold      53
Bifurcation, Hopf      55
Bifurcation, local mode      264—266
Bifurcation, pitchfork      16 52
Bifurcation, saddle-node      109
Bifurcation, subcritical      14
Bifurcation, supercritical      13
Bifurcation, symmetry breaking      98
Billiards      286—287
Birkhoff      98
Bootstrapping      306
Capacity dimension      45—50
Capsize of ships      218—220
Cardiac rhythms      183
Cat maps      299—300
Chaotic saddle, bifurcation      213
Chaotic saddle, catastrophe      211
Chaotic transient      144 210
Chicken pox      171
Codimension      56
Codimension-2 bifurcation      206
Codimension-2 point      58
Congenital rubella syndrome      180
Control parameters      9 54—55 75
Correlation dimension      46—48 158
Coulomb forces      275—276
Coupled difference equations      138—139
Crisis      204
Cycle, heteroclinic      6
Cycle, limit      xii 14
Cycle, Milankovitch      250
Cyclonic 'bombs'      258
Damping      6—7
Daphnia populations      185
Delay differential equation      144
Delays, method of      27—34
Density of states      288
Deterministic chaos      x—xi 85—91
Difference equations, coupled      138—139
Difference equations, exponential      105
Difference equations, quadratic      103
DIMENSION      20
Dimension, capacity      45
Dimension, correlation      46—48 158
Dimension, fractal      21
Discrete Fourier Transform      26
Doubling, period      16—17
Dover cliff phenomenon      116
Dynamical diseases      183—185
Dynamical systems theory      95
EEG pa, terns      184
Eigenvalue      194
El Nino      241
Elastica      51
Embedding dimension      156
Energy balance climate model      249
Engineering integrity      216
Environmental stochasticity      187
Equations, delay-differential      144
Equations, difference      99
Equations, Euler strut      51
Equations, logistic difference      103
Equations, Lorecz's      223
Equations, Mackey — Glass      145
Equations, Mathieu's      9
Equations, Navier — Stokes      69
Equations, ordinary differential      3
Equations, partial differential      70
Equations, Rossler      19
Equatorial waves      238
Equilibrium point      4
Escape scenario      202
Euler strut      51 98
Exponential map      105
Exponents, Lyapunov      42—45 122—123
Fast Fourier Transform      26
Feigenbaum cascade      204
FGGE      235
Fixed point      xi 5
Fixed point, map      103
Fixed point, stable      6 103
Fixed point, unstable      6 103
Flip bifurcation      204
Folding      110—111
Forecasting      155—156
Fourier spectrum      xiii 28—30
Fourier transform      25—26
Fractal, basin boundaries      214—16
Fractal, boundary      201 211
Fractal, dimension      21
Fractal, fingers      216
Fractals in control space      220
Frequency locking      88
Frequency-dependent natural selection      132—138
Gaussian orthogonal ensemble      285
Gaussian unitary ensemble      285
Global atmospheric research programme (GARP)      235
Golden mean      273
Grassberger — Procaccia      158
Gutzwiller trace formula      290—291
Hamiltonian systems, Poincare maps      261—264
harmonic oscillator      3
Harmonics      xiii 26—27
Heteroclinic cycles      6
Hilltop saddle cycle      207
HIV/AIDS      194—198
Homoclinic connection      61—62
Homoclinic orbit      61 91
Homoclinic tangle      211 269—271
Hopf bifurcation      55
Host-parasitoid systems      141
Host-pathogen interactions      178
Hydrodynamic stability      71—73
Hydrogen atom      275—276
Hyperchaotic      144
Hysteresis      14
Ice ages      249—250
Imperfection      53
Incursive fractal      215
Insect populations      188
Instability      10
Intermittency      91
International Whaling Commission - (IWC)      138
Intraseasonal oscillation      234—236
Islands of stability      274
Iterated map      101—103
Julia      98
KAM curves      274
Kelvin wave      238 248
Landau      73
Langford      88
Laplace      97
Length of day (LOD)      235
Limit cycle      xii 14
Limit point      59
Linearized system      ix
Logistic map      103
Lorenz      98—99
Lorenz attractor      222—223
Lyapunov exponents, experimental determination      42—45
Lyapunov exponents, one-dimensional maps      122—124
Lyapunov exponents, two-dimensional maps      144
Lyapunov stability      98
Mackey — Glass equation      145
Magnetic fields      275—276
Mandelbrot      98
Maps, antisymmetric      125—130
Maps, cat      295—300
Maps, coupled      138—144
Maps, cubic      127
Maps, delayed logistic      141
Maps, exponential      105
Maps, iterated      101—103
Maps, logistic      103
Maps, Poincare      33—41 102 261—264
Maps, quadratic      103
Maps, return      38
Maps, tent      153
Maps, two-dimensional      138
Marine plankton      172
Mathieu's equation      9
May      99
Measles, data      158—164
Measles, spatial dynamics      164—171
Method of delays      27—34
Milankovitch cycles      250
Multiplicities      xvi 15 83—84
Navier — Stokes' equations      69—71
Newton      ix 120
Noise      24—25 29
Nonlinear pendulum      3
Nonlinearity      2
Normal mode oscillator      265—266
Number variance      284 297
Numerical bifurcation      14—15
Numerical weather prediction      227—231
Odlyzko      304
Orbit, heteroclinic      6
Orbit, homoclinic      61 91
Orbit, planetary      ix
oscillations      3
Oscillations, clamped      6
Oscillations, intraseasonal      234—236
Oscillations, parametrically excited      8
Oscillations, quasi-biennial      236
Oscillations, simple harmonic      3
Oscillations, southern      243
Palaeoclimatology      249
Parametrically excited pendulum      8—20
Pendulum, simple      2
Period doubling      16 99
Phase bottleneck      272—273
Phase plane      3—5
Phase portrait      3—5
Phase portrait, reconstruction      26—38
Phase space      4—8
Pitchfork bifurcation      13
Planetary orbits      ix
Poincare      97
Poincare maps      38—40 102
Poincare maps, Hamiltonian systems      261—264
Poincare sampling      38 201
Points, equilibrium      4
Points, fixed      xi 5
Points, limit      59
Points, saddle      59
Population dynamics      101 188—192
Population genetics      192
Power spectrum      25—26
Predator prey systems      173
Predictability      7 28—30
Prediction      153—154
Preturbulence      144
Primary resonance      204
Quadratic map      103
Quantum chaology      283
quantum mechanics      282—283
Quasi-biennial oscillation      236
Repeller      7
Resonance      9 266—267
Resonant tongue      10
Return map      38
Return map, stroboscopic      39
Reynolds number      70
Riemann's Zeta-function      392—393
Rossby wave      248
Rossler equations      19
Rotating annulus      254
Ruelle      99
Ruelle — Takens route to chaos      73—74
Saddle focus      62
Saddle point      59
Saddle-node bifurcation      109
Saltzmann      222 249
Semiclassical Berry's theory      293—299 305
Semiclassical limit      282—283
Semiclassical sum rule      295
Sensitive dependence on initial conditions      19—21 120—121 224
Separatrix      6 269
Silnikov      60—67
simple harmonic motion      3
simple pendulum      2—8
Simplex projection      150
Singular value decomposition      34—36
Sloping convection      255
Smale      99
Southern oscillation      243
Spectrum, Fourier      xiii 28—30
Spectrum, power      25—26
Stadium problem      275 292
Strange Attractor      xi 19
Stretching      19
Subcritical bifurcation      14—15
Supercritical Pitchfork bifurcation      13
Symmetry-breaking      16 51—52 81—83 98
Systems, dynamical      96
Systems, Hamiltonian      261
Systems, predator-prey      173
Takens      99
Taylor vortex      74—76
Taylor — Couette flew      74—91
Taylor, G.I.      81
Teleconnections      231—234
Tent map      153
Three-body problem      ix 120
Time series      23—25 149
Time-delayed logistic equation      139—141
Torus      xii 38—41
Trajectory matrix      34
Transient      18 144 210
Transition to turbulence      71—73
Turbulence      93
Universal constants (Feigenbaum)      114
Universality      113—117 284—285
Unstable fixed point      6 103
Unstable solution      13
Vallis attractor      246
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