Bolotin Y., Tur A., Yanovsky V. Chaos: Concepts, Control and Constructive Use
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Index 197
Markov process, 17
maximal Lyapunov exponent, 84
mean-square fluctuations, 34
measure theory, 34
mechano-chemical coupling coefficient, 187
mixed phase space, 97
mobility coefficient, 187
model of coin toss, 17
molecular motor, 185
monotonous complexity, 13
monotonous entropy, 13
multi-body problem, 19
multi-dimensional tunneling, 95
multi-stability, 84
multifractal measure, 34
N
negative feedback, 81
Newton-Rafson procedure, 75
noise, 53
noise level, 84
noise spectrum, 146
noise-induced synchronization, 117
noise-to-signal ratio, 135
non-differentiable function, 44
non-hyperbolic chaotic scattering, 71
non-linear friction, 176
non-linear oscillator model, 78
non-linear pendulum, 62
O
on-off ratchet, 172
Onsager principle, 187
order, 7
over-damped case, 146
P
parameter variation, 54
partial replacement, 105
pass targeting method, 69
passive control, 91
period doubling, 54
period doubling bifurcation, 54
periodic orbit, 19
periodic perturbation, 62
perpetuum mobile, 160
Persival theorem, 146
phase, 22
phase flow, 34
phase space, 14, 19
phase spectrum, 22
phase synchronization, 106
phase transitions, 30
photo-galvanic effect, 174
Poincar
´
e mapping, 19
Poincar
´
e section, 19, 20
power, 13
power spectrum, 145
primitive cell, 186
program, 9
protein, 185
pulsating ratchets, 172
Q
quantum control, 91
quantum system, 91
quasi doublet, 98
quasi-mode, 95
quasi-periodic, 20
quasi-periodic trajectory, 74
R
R
¨
ossler system, 79
random force, 139
random infinite sequences, 12
random sequences, 12
random synchronization, 105
random transition, 137
ratchet model, 160
rational number, 14
recursive function, 13
regular motion, 20
relaxation, 34
resonance overlaps, 69
restricted three-body problem, 70
retraction, 181
reversible mapping, 73
S
saturating perturbation, 84
scale-invariant, 44
scattering region, 71
Schr
¨
odinger equation, 91
secure communication, 101
security level, 129
self-affine fractal, 45
self-control, 87
self-controlled feedback, 81
self-similar set, 45
self-similarity, 44
Smoluchowski equation, 166
Smoluchowski-Feynman gedanken
experiment, 160
Smoluchowski-Feynman model, 163
space-temporal chaos, 122
spectral density, 21
spectrum, 21
spectrum of the Lyapunov exponents, 31
198 Index
square matrix, 28
stability island, 75
stabilization of aperiodic orbit, 88
stable direction, 53, 56
stable manifold, 59
stable node, 32
stable point, 32
stable torus, 32
standard mapping, 108
stationary state, 33
statistical mechanic, 34
statistical physics, 23
sticking effect, 69
stochastic differential equation, 142
stochastic process, 142
stochastic resonance, 135
strange attractor, 32, 41
stroboscopic section, 63
symbolic dynamics, 17
synchronization manifold, 103
synchronization of Hamiltonian systems, 108
T
target function, 91
target orbit, 53
target periodic orbit, 65
targeting, 65
targeting procedure, 65
tent mapping, 29
thermal bath, 187
thermal noise, 163
thermal reservoir, 138
threshold effect, 136
tilting ratchet, 172
time delay, 38
time delay method, 81
time serie, 62
time-dependent environment, 78
topological dimension, 42
trace formula, 52
trajectory, 25
transition probabiliti, 143
transition process, 84
transitive system, 18
transport phenomena, 159
traveling potential ratchet, 172
tunneling effect, 93
tunneling rate, 92
Turing machine, 9
two-state model, 142, 187
U
umbrella’s equation, 176
unity matrix, 28
universal sequential test, 13
universal Turing machine, 11
unstable direction, 53, 56
unstable fixed point, 53
unstable periodic orbits, 52
wave function, 91
wave packet, 92
Weierstrass function, 44
whispering gallery trajectory, 96
white noise, 136
W