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Haken H. — Synergetics: an introduction
Haken H. — Synergetics: an introduction

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Название: Synergetics: an introduction

Автор: Haken H.

Аннотация:

This book is an often-requested reprint of two classic texts by H. Haken: "Synergetics. An Introduction" and "Advanced Synergetics". Synergetics, an interdisciplinary research program initiated by H. Haken in 1969, deals with the systematic and methodological approach to the rapidly growing field of complexity. Going well beyond qualitative analogies between complex systems in fields as diverse as physics, chemistry, biology, sociology and economics, Synergetics uses tools from theoretical physics and mathematics to construct an unifying framework within which quantitative descriptions of complex, self-organizing systems can be made. This may well explain the timelessness of H. Haken's original texts on this topic, which are now recognized as landmarks in the field of complex systems. They provide both the beginning graduate student and the seasoned researcher with solid knowledge of the basic concepts and mathematical tools. Moreover, they admirably convey the spirit of the pioneering work by the founder of Synergetics through the essential applications contained herein that have lost nothing of their paradigmatic character since they were conceived.


Язык: en

Рубрика: Физика/Нелинейная динамика, Хаос/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1977

Количество страниц: 325

Добавлена в каталог: 11.09.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abundance of species      293
Adaptability      200 202
Affinity      60
Approximation, adiabalic      192 195 196 198
Associativity (of sets)      19
Autocatalytic process      300
Autocatalytic reaction      107 128 263
Autonomous system      113
Average over ensemble      100
Balls in boxes      46
Bandwidth      153
Belousov — Zhabotinski reaction      9 276
Benard instability      7 244
Bifurcation      110 126
Bifurcation of limit cycles      112
Binary system      42
Binomial coefficient      33
Binomial distribution      33 34
Binomial distribution, mean value      34
Binomial distribution, variance      34
Biochemical systems      263
Birth and death processes      277 282
Bistable element      290
Bit      42
Boltzmann distribution function      54
Boltzmann distribution of harmonic oscillator      156
Boltzmann's H-theorem      126
Boussinesq approximation      245
box model      33
Browman movement      69 149
Browman movement, distribution function      73
Brusselator      211 270
Brusselator, stochastic treatment      286
Catastrophe      133
Center      117 118
Central limit theorem      39
Chapman — Kolmogorov equation      79 81
Characteristic function      31 85 86
Characteristic function, derivatives      32 33
Chemical network      290
chemical potential      56
Chemical reaction, stochastic model      277 282
chemical systems      263
Chetayev's instability theorem      125
Cloud formation      7 8
Cloud streets      8
Coarse graining      66
Coexistence of species      129 294
Commutativity (of intersection of sets)      19
Commutativity (of union of sets)      19
Competition of species      294
Complement (of a set)      19
Constants of motion      165
Constraint      45 48
Continuity equation      63
Continuity equation of probability      160
Continuity equation of probability distribution      166
Continuous mode laser      233
Convection instability      7 244
Coordinates, Cartesian      111
Coordinates, polar      111
Correlation      31
Correlation function      87
Correlation function of fluctuating forces      149 151 187 188
Correlation function, two point      187 188
Correlation function, two time      150 173
Correlation, length      188
critical exponent      188
Critical fluctuations of laser      230
Critical point      113
Critical slowing down      110 181
Cumulants      86 152
De Morgan's law      19
Density function      24
Detailed balance      89
Detailed balance in chemical reactions      280
Detailed balance, counterexample to      91
Detailed balance, principle      77 95
Dictyostelium disciodeum      9
Diffusion      268
Diffusion coefficient      163
Diffusion constant      71
Diffusion equation      78 83
Diffusion process, correlation functions      87
Diffusion, stochastic model      282
Dirac's $\delta$-function      25
Disorder      1
Dissipation-fluctuation theorem, example      150
Dissipative structures      309
distribution      21 23
Distribution function      23
Distributivity (of set relations)      19
Drift-coefficient      163
Dynamic processes      105
Dynamic system theory      308
Ecology      293
Ehrenfest urn model      98
Elastic stability      257
Elimination in Fokker — Planck equation, adiabatic      202
Elimination in master equation, adiabatic      204
Energy, degradation      2
Energy, internal      54
Ensemble      100
entropy      2 54 66 101
Entropy density      63
Entropy density, continuity equation      64
Entropy flux      64
Entropy, additivity      65
Entropy, coarse grained      66
Entropy, production rate      64
Equilibrium points      108 109 114
Equilibrium, thermodynamic      100
Event, simple      17
Evolution      298
Excitation transfer by hopping process      78
Expectation, mathematical      28
Extensive variables      58 60
Ferromagnet      3 179
First passage time problem      169
Flip-flop      291
Fluctuating forces, correlation function of      149 151 187 188
Fluctuations      98 100
Fluctuations in self-organization      200
Fluid, flow of      6
Flux equilibrium      307
Focus      117 118
Focus, stable      112 118
Focus, unstable      111 112 118
Fokker — Planck equation      78 158 163 202
Fokker — Planck of convection instability      249
Fokker — Planck of many variables      164
Fokker — Planck of multimode laser, solution of      233 234
Fokker — Planck of single mode laser      230
Fokker — Planck, derivation      160
Fokker — Planck, functional      187 188
Fokker — Planck, stationary solution      165—167 171 187 188
Fokker — Planck, time-dependent solutions      172 174
Force, friction      147 153
Forces, fluctuating(random), Gaussian distribution      151
Forces, fluctuating, correlation functions      156 157
Forces, random      152
Free energy      54 57 179 186
Friction force      105
Gambling machine with binomial distribution      74
Gas atoms in box      44
Gaussian distribution      37
Gaussian probability density of several variables      38
Gaussian probability density, characteristic functions      39
Gaussian probability density, first moment      39
Gaussian probability density, mean      38
Gaussian probability density, moments      39
Gaussian probability density, second moment      39
Gaussian probability density, variance      38
Gaussian process      85 86
General systems theory      307
Generating function      31
Ginzburg functional      186
Ginzburg theory of superconductivity      235
Ginzburg — Landau equation, generalized      206-215
Ginzburg — Landau, time dependent      187 216
graphs      95
Graphs, examples      96
Green's function      218
Green's function of Fokker — Planck equation      173 174
Growth, density-dependent      294
Growth, density-independent      294
Gunn instability      253
H-Theorem      126
Half-trajectory      119
Hamiltonian equations      165
Hard excitation      112
Hard mode      112
Hard mode instability      218 222
Harmonic oscillator at different temperatures      157
Harmonic oscillator coupled to reservoirs      153
Harmonic oscillator, coupled, Hamiltonian      158
Heat      56
Heat flow      64
Heat, generalized      52 56
Hexagon formation in fluids      251
Hurwitz criterion      123
Hydra      299
Hypothesis      30
Hysteresis      182
information      41
Information entropy      48
Information entropy as solution of Liouville equation      165
Information entropy of population      46
Information entropy, variational principle for      49
Information gain      46 48 126
Information per symbol      43
Information, extremal condition for      44
Inhibition      299
Instabilities in fluid dynamics      244
Instabilities in lasers      239
Instabilities, classification      133
Instabilities, symmetry breaking      110
Invariance      109
inversion      109
Irreversible expansion of a gas      1
Irreversible heat exchange      1
Irreversible process      101 102
Irreversible thermodynamics      57
Irreversible thermodynamics, limitations      102
Joint probability of time-dependent processes      75 76
Lagrange parameters      49
Lagrangian multipliers      45
Landau theory of phase transitions      180
Langevin equation      147 162 163 168 169 187 188
Langevin equation of fluids      249
Laser      4—6 127 225
Laser equations      226
Laser phase transition      225 230
Laser phase transition analogy      307
Laser pulses, ultrashort      239
Laser threshold      128
Laser, two-mode      128 129
Likelihood, equal      21
Limit cycle      110 113 119
Limit cycle, stable      111 112
Limit cycle, unstable      111 112
Liouville equation      165
Ljapunov function      124
Ljapunov function, examples for      131 132
Ljapunov instability theorem      125
Ljapunov stability theorem      125
Lotka model      130 131
Lotka — Volterra equations      296
Lotka — Volterra, stochastic treatment      297
magnetization      3 179
Malfunctioning, suppression      202
Markov process      79 80
Mass action, law of      279
Master equation      75 83 88 204
Master equation for chemical reaction      277 286
Master equation for chemical reaction, stationary solution      279
Master equation with detailed balance      92
Master equation with detailed balance, stationary solution      89
Master equation, Kirchhoff's method of solution of      95
Master equation, Ljapunov function of      126
Master equation, theorems about solutions of      97
Maxwell's construction      270
Mean      28
Mean value      28
Memory      201
memory device      201
Microreversibility      126
MODE      14 15
Moments      29 33 85 152
Moments, time-dependent      173
Morphogenesis      299
Multimode laser      231
Network, chemical      290
Network, electrical      290
Newton's law      105
Niche, ecological      295
Node      115 116
Nonautonomous system      126
Nonequilibrium phase transition      206
Nonequilibrium phase transition of chemical reactions      289
Normal distribution      37
Normal distribution of several variables      38
Onsager coefficients      64
Order      1
Order parameter      14 15 180 195 198 199 227 303 307
Order parameter, space dependent      186
Oregonator      270 276
ORGANIZATION      191
Oscillations in biology      9 11
Oscillator      106
Oscillator, anharmonic      108
Oscillator, harmonic      152
Oscillator, overdamped      107
Overdamped motion      106
Parameters, external      15
Partition function      50 54 56
Partition function, variational principle for      52 53
path integral      79 83 84 176
Path integral, solution of Fokker — Planck equation      176
Paths      79
Phase plane      113
Phase transition      3 179
Phase transition analogy      179 184
Phase transition analogy for convection instability      252
Phase transition analogy for lasers      230 235
Phase transition analogy in continuous media      186
Phase transition of chemical reactions      265 266 284
Phase transition, continuous      186
Phase transition, first order      182
Phase transition, first order, of single-mode laser      236
Phase transition, Landau theory      181 185
Phase transition, second order      181
Phases      2 3
Poincare — Bendixson theorem      119
Poisson distribution      35 36 92
Poisson distribution of molecules      281
Poisson distribution, generating function      36
Poisson distribution, mathematical expectation      36
Poisson distribution, variance of      36
Polarization of public opinion      305
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