Synchronization: a universal concept in nonlinear sciences
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2007
|
| Ausgabe: | 1. paperback ed. |
| Schriftenreihe: | Cambridge nonlinear science series
12 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIX, 411 S. Ill., graph. Darst. |
| ISBN: | 9780521533522 0521592852 |
Internformat
MARC
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| 100 | 1 | |a Pikovskij, Arkadij |d 1956- |e Verfasser |0 (DE-588)140665773 |4 aut | |
| 245 | 1 | 0 | |a Synchronization |b a universal concept in nonlinear sciences |
| 250 | |a 1. paperback ed. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2007 | |
| 300 | |a XIX, 411 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Cambridge nonlinear science series |v 12 | |
| 650 | 0 | 7 | |a Oszillator |0 (DE-588)4132814-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Synchronisierung |0 (DE-588)4130847-5 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Synchronisierung |0 (DE-588)4130847-5 |D s |
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| 689 | 1 | 0 | |a Oszillator |0 (DE-588)4132814-0 |D s |
| 689 | 1 | |5 DE-604 | |
| 700 | 1 | |a Rosenblum, Michael G. |e Verfasser |4 aut | |
| 700 | 1 | |a Kurths, Jürgen |d 1953- |e Verfasser |0 (DE-588)11022714X |4 aut | |
| 830 | 0 | |a Cambridge nonlinear science series |v 12 |w (DE-604)BV004573757 |9 12 | |
| 856 | 4 | 2 | |m Digitalisierung UB Passau |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016470321&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
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Datensatz im Suchindex
| _version_ | 1804137606371344384 |
|---|---|
| adam_text | Contents
Preface
xvii
Chapter
1
Introduction
1
1.1
Synchronization in historical perspective
1
1.2
Synchronization: just a description
7
1.2.1
What is synchronization?
8
1.2.2
What is NOT synchronization
? 14
1.3
Synchronization: an overview of different cases
18
1.3.1
Terminological remarks
22
1.4
Main bibliography
23
Part I: Synchronization without formulae
Chapter
2
Basic notions: the self-sustained oscillator and its phase
27
2.1
Self-sustained oscillators: mathematical models of natural systems
28
2.1.1
Self-sustained oscillations are typical in nature
28
2.1.2
Geometrical image of periodic self-sustained oscillations: limit cycle
29
2.2
Phase: definition and properties
31
2.2.1
Phase and amplitude of
a
quasilinear
oscillator
31
2.2.2
Amplitude is stable, phase is free
32
2.2.3
General case: limit cycle of arbitrary shape
33
2.3
Self-sustained oscillators: main features
35
2.3.1
Dissipation, stability and nonlinearity
35
2.3.2
Autonomous and forced systems: phase of a forced system is not free!
38
2.4
Self-sustained oscillators: further examples and discussion
40
2.4.1
Typical self-sustained system: internal feedback loop
40
2.4.2
Relaxation
oscillators
41
Chapter
3
Synchronization of a periodic oscillator by external force
45
3.1
Weakly forced
quasilinear
oscillators
46
3.1.1
The autonomous oscillator and the force in the rotating reference
f
rame
46
3.1.2
Phase and frequency locking
49
3.1.3
Synchronization transition
53
3.1.4
An example: entrainment of respiration by a mechanical ventilator
56
3.2
Synchronization by external force: extended discussion
59
3.2.1
Stroboscopie
observation
59
3.2.2
An example: periodically stimulated firefly
61
3.2.3
Entrainment by a pulse train
62
3.2.4
Synchronization of higher order. Arnold tongues
65
3.2.5
An example: periodic stimulation ofatrial pacemaker cells
67
3.2.6
Phase and frequency locking: general formulation
67
3.2.7
An example: synchronization of a laser
69
3.3
Synchronization of relaxation oscillators: special features
71
3.3.1
Resetting by external pulses. An example: the cardiac pacemaker
71
3.3.2
Electrical model of the heart by van
der
Pol and van
der
Mark
72
3.3.3
Variation of the threshold. An example: the electronic relaxation oscillator
73
3.3.4
Variation of the natural frequency
76
3.3.5
Modulation vs. synchronization
77
3.3.6
An example: synchronization of the songs of snowy tree cricks
78
3.4
Synchronization in the presence of noise
79
3.4.1
Phase diffusion in a noisy oscillator
80
3.4.2
Forced noisy oscillators. Phase slips
81
3.4.3
An example: entrainment of respiration by mechanical ventilation
85
3.4.4
An example: entrainment of the cardiac rhythm by weak external stimuli
85
3.5
Diverse examples
86
3.5.1
Circadian rhythms
86
3.5.2
The menstrual cycle
88
3.5.3
Entrainment of pulsatile insulin secretion by oscillatory glucose infusion
89
3.5.4
Synchronization in protoplasmic strands of Physarum
90
3.6
Phenomena around synchronization
90
3.6.1
Related effects at strong external forcing
91
3.6.2
Stimulation of excitable systems
93
3.6.3
Stochastic resonance from the synchronization viewpoint
94
3.6.4
Entrainment of several oscillators by a common drive
98
Chapter
4
Synchronization of two and many oscillators
102
4.1
Mutual synchronization of self-sustained oscillators
102
4.1.1
Two interacting oscillators
103
4.1.2
An example: synchronization of
triode
generators
105
4.1.3
An example: respiratory and wing beat frequency of free-flying barnacle
geese
107
4.1.4
An example: transition between in-phase and anti-phase motion
108
4.1.5
Concluding remarks and related effects
110
4.1.6
Relaxation oscillators. An example: true and latent pacemaker cells in the
sino-atrial node 111
4.1.7
Synchronization of noisy systems. An example: brain and muscle activity of a
Parkinsonian patient
112
4.1.8
Synchronization of rotators. An example:
Josephson
junctions
114
4.1.9
Several oscillators
117
4.2
Chains, lattices and oscillatory media
119
4.2.1
Synchronization in a lattice. An example: laser arrays
119
4.2.2
Formation of clusters. An example: electrical activity of mammalian
intestine
121
4.2.3
Clusters and beats in a medium: extended discussion
122
4.2.4
Periodically forced oscillatory medium. An example: forced
Belousov-Zhabotinsky reaction
124
4.3
Globally coupled oscillators
126
4.3.1
Kuramoto self-synchronization transition
126
4.3.2
An example: synchronization of menstrual cycles
129
4.3.3
An example: synchronization of glycolytic oscillations in a population of
yeast cells
130
4.3.4
Experimental study of rhythmic hand clapping
131
4.4
Diverse examples
131
4.4.1
Running and breathing in mammals
131
4.4.2
Synchronization of two salt-water oscillators
133
4.4.3
Entrainment of tubular pressure oscillations in nephrons
133
4.4.4
Populations of cells
133
4.4.5
Synchronization of predator-prey cycles
134
4.4.6
Synchronization in
neuronal
systems
134
Chapter
5
Synchronization of chaotic systems
137
5.1
Chaotic oscillators
137
5.1.1
An exemplar: the
Lorenz
model
138
5.1.2
Sensitive dependence on initial conditions
140
5.2
Phase
synchronization of chaotic oscillators
141
5.2.1
Phase and average frequency of a chaotic oscillator
142
5.2.2
Entrainment by a periodic force. An example: forced chaotic plasma
discharge
144
5.3
Complete synchronization of chaotic oscillators
147
5.3.1
Complete synchronization of identical systems. An example:
synchronization of two lasers
148
5.3.2
Synchronization of nonidentical systems
149
5.3.3
Complete synchronization in a general context. An example: synchronization
and clustering of globally coupled electrochemical oscillators
150
5.3.4
Chaos-destroying synchronization
152
Chapter
6
Detecting synchronization in experiments
153
6.1
Estimating phases and frequencies from data
153
6.1.1
Phase of a spike train. An example: electrocardiogram
154
6.1.2
Phase of a narrow-band signal. An example: respiration
155
6.1.3
Several practical remarks
155
6.2
Data analysis in active and passive experiments
156
6.2.1
Active experiment
156
6.2.2
Passive experiment
157
6.3
Analyzing relations between the phases
160
6.3.1
Straightforward analysis of the phase difference. An example: posture control
in humans
160
6.3.2
High level of noise
163
6.3.3
Stroboscopic
technique
163
6.3.4
Phase
stroboscope
in the case
ηΩ|
^
тЧ^і-
An example: cardiorespiratory
interaction
164
6.3.5
Phase relations in the case of strong modulation. An example: spiking of
electroreceptors of a paddlefish
166
6.4
Concluding remarks and bibliographic notes
168
6.4.1
Several remarks on passive experiments
168
6.4.2
Quantification and significance of phase relation analysis
170
6.4.3
Some related references
171
Part II: Phase locking and frequency entrainment
Chapter
7
Synchronization of periodic oscillators by periodic external
action
175
7.1
Phase dynamics
176
7.1.1
A limit cycle and the phase of oscillations
176
7.1.2
Small perturbations and
isochrones 177
7.1.3
An example: complex amplitude equation
179
7.1.4
The equation
f
or the phase dynamics
180
7.1.5
An example: forced complex amplitude equations
181
7.1.6
Slow phase dynamics
182
7.1.7
Slow phase dynamics: phase locking and synchronization region
184
7.1.8
Summary of the phase dynamics
187
7.2
Weakly nonlinear oscillator
189
7.2.1
The amplitude equation
189
7.2.2
Synchronization properties: isochronous case
192
7.2.3
Synchronization properties: nonisochronous case
198
7.3
The circle and annulus map
199
7.3.1
The circle map: derivation and examples
201
7.3.2
The circle map: properties
204
7.3.3
The annulus map
210
7.3.4
Large force and transition to chaos
213
7.4
Synchronization of rotators and
Josephson
junctions
215
7.4.1
Dynamics of rotators and
Josephson
junctions
215
7.4.2
Overdamped rotator in an external field
217
7.5
Phase locked loops
218
7.6
Bibliographic notes
221
Chapter
8
Mutual synchronization of two interacting periodic
oscillators
222
8.1
Phase dynamics
222
8.1.1
Averaged equations for the phase
224
8.1.2
Circle map
226
8.2
Weakly nonlinear oscillators
227
8.2.1
General equations
227
8.2.2
Oscillation death, or quenching
229
8.2.3
Attractive and repulsive interaction
230
8.3
Relaxation oscillators
232
8.4
Bibliographic notes
235
Chapter
9
Synchronization in the presence of noise
236
9.1
Self-sustained oscillator in the presence of noise
236
9.2
Synchronization in the presence of noise
237
9.2.1
Qualitative picture of the
Langevin
dynamics
237
9.2.2
Quantitative description for white noise
240
9.2.3
Synchronization by a quasiharmonic fluctuating force
244
9.2.4
Mutual synchronization of noisy oscillators
245
9.3
Bibliographic notes
246
Chapter
10
Phase synchronization of chaotic systems
247
10.1
Phase of a chaotic oscillator
248
10.1.1
Notion of the phase
248
10.1.2
Phase dynamics of chaotic oscillators
254
10.2
Synchronization of chaotic oscillators
255
10.2.1
Phase synchronization by external force
256
10.2.2
Indirect characterization of synchronization
258
10.2.3
Synchronization in terms of unstable periodic orbits
260
10.2.4
Mutual synchronization of two coupled oscillators
262
10.3
Bibliographic notes
263
Chapter
11
Synchronization in oscillatory media
266
11.1
Oscillator lattices
266
11.2
Spatially continuous phase profiles
269
11.2.1
Plane waves and targets
269
11.2.2
Effect of noise: roughening vs. synchronization
271
11.3
Weakly nonlinear oscillatory medium
273
11.3.1
Complex Ginzburg-Landau equation
273
11.3.2
Forcing oscillatory media
276
11.4
Bibliographic notes
278
Chapter
12
Populations of globally coupled oscillators
279
12.1
The Kuramoto transition
279
12.2
Noisy oscillators
283
12.3
Generalizations
286
12.3.1
Models based on phase approximation
286
12.3.2
Globally coupled weakly nonlinear oscillators
289
12.3.3
Coupled relaxation oscillators
290
12.3.4
Coupled
Josephson
junctions
291
12.3.5
Finite-size effects
294
12.3.6
Ensemble of chaotic oscillators
294
12.4
Bibliographic notes
296
Part III: Synchronization of chaotic systems
Chapter
13
Complete synchronization I: basic concepts
301
13.1
The simplest model: two coupled maps
302
13.2
Stability of the synchronous state
304
13.3
Onset of synchronization: statistical theory
307
13.3.1
Perturbation is a random walk process
307
13.3.2
The statistics of finite-time Lyapunov exponents determine diffusion
308
13.3.3
Modulational intermittency: power-law distributions
310
13.3.4
Modulational intermittency: correlation properties
316
13.4
Onset of synchronization: topological aspects
318
13.4.1
Transverse bifurcations of periodic orbits
318
13.4.2
Weak vs. strong synchronization
319
13.4.3
Local and global riddling
322
13.5
Bibliographic notes
323
Chapter
14
Complete synchronization II: generalizations and complex
systems
324
14.1
Identical maps, general coupling operator
324
14.1.1
Unidirectional coupling
325
14.1.2
Asymmetric local coupling
327
14.1.3
Global (mean field) coupling
328
14.2
Continuous-time systems
329
14.3
Spatially distributed systems
331
14.3.1
Spatially homogeneous chaos
331
14.3.2
Transverse synchronization of space-time chaos
332
14.3.3
Synchronization of coupled cellular automata
334
14.4
Synchronization as a general symmetric state
335
14.4.1
Replica-symmetric systems
336
14.5
Bibliographic notes
337
Chapter
15
Synchronization of complex dynamics by external forces
340
15.1
Synchronization by periodic forcing
341
15.2
Synchronization by noisy forcing
341
15.2.1
Noisy forced periodic oscillations
343
15.2.2
Synchronization of chaotic oscillations by noisy forcing
345
15.3
Synchronization of chaotic oscillations by chaotic forcing
346
15.3.1
Complete synchronization
346
15.3.2
Generalized synchronization
347
15.3.3
Generalized synchronization by quasiperiodic driving
352
15.4
Bibliographic notes
353
Appendices
Appendix
Al:
Discovery of synchronization by Christiaan Huygens
357
A
1.1
A letter from Christiaan Huygens to his father, Constantyn Huygens
357
A
1.2
Sea clocks (sympathy of clocks). Part V
358
Appendix A2: Instantaneous phase and frequency of a signal
362
A2.1 Analytic signal and the Hubert transform
362
A2.2 Examples
363
A2.3 Numerics: practical hints and know-hows
366
A2.4 Computation of the instantaneous frequency
369
References
371
Index
405
|
| adam_txt |
Contents
Preface
xvii
Chapter
1
Introduction
1
1.1
Synchronization in historical perspective
1
1.2
Synchronization: just a description
7
1.2.1
What is synchronization?
8
1.2.2
What is NOT synchronization
? 14
1.3
Synchronization: an overview of different cases
18
1.3.1
Terminological remarks
22
1.4
Main bibliography
23
Part I: Synchronization without formulae
Chapter
2
Basic notions: the self-sustained oscillator and its phase
27
2.1
Self-sustained oscillators: mathematical models of natural systems
28
2.1.1
Self-sustained oscillations are typical in nature
28
2.1.2
Geometrical image of periodic self-sustained oscillations: limit cycle
29
2.2
Phase: definition and properties
31
2.2.1
Phase and amplitude of
a
quasilinear
oscillator
31
2.2.2
Amplitude is stable, phase is free
32
2.2.3
General case: limit cycle of arbitrary shape
33
2.3
Self-sustained oscillators: main features
35
2.3.1
Dissipation, stability and nonlinearity
35
2.3.2
Autonomous and forced systems: phase of a forced system is not free!
38
2.4
Self-sustained oscillators: further examples and discussion
40
2.4.1
Typical self-sustained system: internal feedback loop
40
2.4.2
Relaxation
oscillators
41
Chapter
3
Synchronization of a periodic oscillator by external force
45
3.1
Weakly forced
quasilinear
oscillators
46
3.1.1
The autonomous oscillator and the force in the rotating reference
f
rame
46
3.1.2
Phase and frequency locking
49
3.1.3
Synchronization transition
53
3.1.4
An example: entrainment of respiration by a mechanical ventilator
56
3.2
Synchronization by external force: extended discussion
59
3.2.1
Stroboscopie
observation
59
3.2.2
An example: periodically stimulated firefly
61
3.2.3
Entrainment by a pulse train
62
3.2.4
Synchronization of higher order. Arnold tongues
65
3.2.5
An example: periodic stimulation ofatrial pacemaker cells
67
3.2.6
Phase and frequency locking: general formulation
67
3.2.7
An example: synchronization of a laser
69
3.3
Synchronization of relaxation oscillators: special features
71
3.3.1
Resetting by external pulses. An example: the cardiac pacemaker
71
3.3.2
Electrical model of the heart by van
der
Pol and van
der
Mark
72
3.3.3
Variation of the threshold. An example: the electronic relaxation oscillator
73
3.3.4
Variation of the natural frequency
76
3.3.5
Modulation vs. synchronization
77
3.3.6
An example: synchronization of the songs of snowy tree cricks
78
3.4
Synchronization in the presence of noise
79
3.4.1
Phase diffusion in a noisy oscillator
80
3.4.2
Forced noisy oscillators. Phase slips
81
3.4.3
An example: entrainment of respiration by mechanical ventilation
85
3.4.4
An example: entrainment of the cardiac rhythm by weak external stimuli
85
3.5
Diverse examples
86
3.5.1
Circadian rhythms
86
3.5.2
The menstrual cycle
88
3.5.3
Entrainment of pulsatile insulin secretion by oscillatory glucose infusion
89
3.5.4
Synchronization in protoplasmic strands of Physarum
90
3.6
Phenomena around synchronization
90
3.6.1
Related effects at strong external forcing
91
3.6.2
Stimulation of excitable systems
93
3.6.3
Stochastic resonance from the synchronization viewpoint
94
3.6.4
Entrainment of several oscillators by a common drive
98
Chapter
4
Synchronization of two and many oscillators
102
4.1
Mutual synchronization of self-sustained oscillators
102
4.1.1
Two interacting oscillators
103
4.1.2
An example: synchronization of
triode
generators
105
4.1.3
An example: respiratory and wing beat frequency of free-flying barnacle
geese
107
4.1.4
An example: transition between in-phase and anti-phase motion
108
4.1.5
Concluding remarks and related effects
110
4.1.6
Relaxation oscillators. An example: true and latent pacemaker cells in the
sino-atrial node 111
4.1.7
Synchronization of noisy systems. An example: brain and muscle activity of a
Parkinsonian patient
112
4.1.8
Synchronization of rotators. An example:
Josephson
junctions
114
4.1.9
Several oscillators
117
4.2
Chains, lattices and oscillatory media
119
4.2.1
Synchronization in a lattice. An example: laser arrays
119
4.2.2
Formation of clusters. An example: electrical activity of mammalian
intestine
121
4.2.3
Clusters and beats in a medium: extended discussion
122
4.2.4
Periodically forced oscillatory medium. An example: forced
Belousov-Zhabotinsky reaction
124
4.3
Globally coupled oscillators
126
4.3.1
Kuramoto self-synchronization transition
126
4.3.2
An example: synchronization of menstrual cycles
129
4.3.3
An example: synchronization of glycolytic oscillations in a population of
yeast cells
130
4.3.4
Experimental study of rhythmic hand clapping
131
4.4
Diverse examples
131
4.4.1
Running and breathing in mammals
131
4.4.2
Synchronization of two salt-water oscillators
133
4.4.3
Entrainment of tubular pressure oscillations in nephrons
133
4.4.4
Populations of cells
133
4.4.5
Synchronization of predator-prey cycles
134
4.4.6
Synchronization in
neuronal
systems
134
Chapter
5
Synchronization of chaotic systems
137
5.1
Chaotic oscillators
137
5.1.1
An exemplar: the
Lorenz
model
138
5.1.2
Sensitive dependence on initial conditions
140
5.2
Phase
synchronization of chaotic oscillators
141
5.2.1
Phase and average frequency of a chaotic oscillator
142
5.2.2
Entrainment by a periodic force. An example: forced chaotic plasma
discharge
144
5.3
Complete synchronization of chaotic oscillators
147
5.3.1
Complete synchronization of identical systems. An example:
synchronization of two lasers
148
5.3.2
Synchronization of nonidentical systems
149
5.3.3
Complete synchronization in a general context. An example: synchronization
and clustering of globally coupled electrochemical oscillators
150
5.3.4
Chaos-destroying synchronization
152
Chapter
6
Detecting synchronization in experiments
153
6.1
Estimating phases and frequencies from data
153
6.1.1
Phase of a spike train. An example: electrocardiogram
154
6.1.2
Phase of a narrow-band signal. An example: respiration
155
6.1.3
Several practical remarks
155
6.2
Data analysis in "active" and "passive" experiments
156
6.2.1
"Active" experiment
156
6.2.2
"Passive" experiment
157
6.3
Analyzing relations between the phases
160
6.3.1
Straightforward analysis of the phase difference. An example: posture control
in humans
160
6.3.2
High level of noise
163
6.3.3
Stroboscopic
technique
163
6.3.4
Phase
stroboscope
in the case
ηΩ|
^
тЧ^і-
An example: cardiorespiratory
interaction
164
6.3.5
Phase relations in the case of strong modulation. An example: spiking of
electroreceptors of a paddlefish
166
6.4
Concluding remarks and bibliographic notes
168
6.4.1
Several remarks on "passive" experiments
168
6.4.2
Quantification and significance of phase relation analysis
170
6.4.3
Some related references
171
Part II: Phase locking and frequency entrainment
Chapter
7
Synchronization of periodic oscillators by periodic external
action
175
7.1
Phase dynamics
176
7.1.1
A limit cycle and the phase of oscillations
176
7.1.2
Small perturbations and
isochrones 177
7.1.3
An example: complex amplitude equation
179
7.1.4
The equation
f
or the phase dynamics
180
7.1.5
An example: forced complex amplitude equations
181
7.1.6
Slow phase dynamics
182
7.1.7
Slow phase dynamics: phase locking and synchronization region
184
7.1.8
Summary of the phase dynamics
187
7.2
Weakly nonlinear oscillator
189
7.2.1
The amplitude equation
189
7.2.2
Synchronization properties: isochronous case
192
7.2.3
Synchronization properties: nonisochronous case
198
7.3
The circle and annulus map
199
7.3.1
The circle map: derivation and examples
201
7.3.2
The circle map: properties
204
7.3.3
The annulus map
210
7.3.4
Large force and transition to chaos
213
7.4
Synchronization of rotators and
Josephson
junctions
215
7.4.1
Dynamics of rotators and
Josephson
junctions
215
7.4.2
Overdamped rotator in an external field
217
7.5
Phase locked loops
218
7.6
Bibliographic notes
221
Chapter
8
Mutual synchronization of two interacting periodic
oscillators
222
8.1
Phase dynamics
222
8.1.1
Averaged equations for the phase
224
8.1.2
Circle map
226
8.2
Weakly nonlinear oscillators
227
8.2.1
General equations
227
8.2.2
Oscillation death, or quenching
229
8.2.3
Attractive and repulsive interaction
230
8.3
Relaxation oscillators
232
8.4
Bibliographic notes
235
Chapter
9
Synchronization in the presence of noise
236
9.1
Self-sustained oscillator in the presence of noise
236
9.2
Synchronization in the presence of noise
237
9.2.1
Qualitative picture of the
Langevin
dynamics
237
9.2.2
Quantitative description for white noise
240
9.2.3
Synchronization by a quasiharmonic fluctuating force
244
9.2.4
Mutual synchronization of noisy oscillators
245
9.3
Bibliographic notes
246
Chapter
10
Phase synchronization of chaotic systems
247
10.1
Phase of a chaotic oscillator
248
10.1.1
Notion of the phase
248
10.1.2
Phase dynamics of 'chaotic oscillators
254
10.2
Synchronization of chaotic oscillators
255
10.2.1
Phase synchronization by external force
256
10.2.2
Indirect characterization of synchronization
258
10.2.3
Synchronization in terms of unstable periodic orbits
260
10.2.4
Mutual synchronization of two coupled oscillators
262
10.3
Bibliographic notes
263
Chapter
11
Synchronization in oscillatory media
266
11.1
Oscillator lattices
266
11.2
Spatially continuous phase profiles
269
11.2.1
Plane waves and targets
269
11.2.2
Effect of noise: roughening vs. synchronization
271
11.3
Weakly nonlinear oscillatory medium
273
11.3.1
Complex Ginzburg-Landau equation
273
11.3.2
Forcing oscillatory media
276
11.4
Bibliographic notes
278
Chapter
12
Populations of globally coupled oscillators
279
12.1
The Kuramoto transition
279
12.2
Noisy oscillators
283
12.3
Generalizations
286
12.3.1
Models based on phase approximation
286
12.3.2
Globally coupled weakly nonlinear oscillators
289
12.3.3
Coupled relaxation oscillators
290
12.3.4
Coupled
Josephson
junctions
291
12.3.5
Finite-size effects
294
12.3.6
Ensemble of chaotic oscillators
294
12.4
Bibliographic notes
296
Part III: Synchronization of chaotic systems
Chapter
13
Complete synchronization I: basic concepts
301
13.1
The simplest model: two coupled maps
302
13.2
Stability of the synchronous state
304
13.3
Onset of synchronization: statistical theory
307
13.3.1
Perturbation is a random walk process
307
13.3.2
The statistics of finite-time Lyapunov exponents determine diffusion
308
13.3.3
Modulational intermittency: power-law distributions
310
13.3.4
Modulational intermittency: correlation properties
316
13.4
Onset of synchronization: topological aspects
318
13.4.1
Transverse bifurcations of periodic orbits
318
13.4.2
Weak vs. strong synchronization
319
13.4.3
Local and global riddling
322
13.5
Bibliographic notes
323
Chapter
14
Complete synchronization II: generalizations and complex
systems
324
14.1
Identical maps, general coupling operator
324
14.1.1
Unidirectional coupling
325
14.1.2
Asymmetric local coupling
327
14.1.3
Global (mean field) coupling
328
14.2
Continuous-time systems
329
14.3
Spatially distributed systems
331
14.3.1
Spatially homogeneous chaos
331
14.3.2
Transverse synchronization of space-time chaos
332
14.3.3
Synchronization of coupled cellular automata
334
14.4
Synchronization as a general symmetric state
335
14.4.1
Replica-symmetric systems
336
14.5
Bibliographic notes
337
Chapter
15
Synchronization of complex dynamics by external forces
340
15.1
Synchronization by periodic forcing
341
15.2
Synchronization by noisy forcing
341
15.2.1
Noisy forced periodic oscillations
343
15.2.2
Synchronization of chaotic oscillations by noisy forcing
345
15.3
Synchronization of chaotic oscillations by chaotic forcing
346
15.3.1
Complete synchronization
346
15.3.2
Generalized synchronization
347
15.3.3
Generalized synchronization by quasiperiodic driving
352
15.4
Bibliographic notes
353
Appendices
Appendix
Al:
Discovery of synchronization by Christiaan Huygens
357
A
1.1
A letter from Christiaan Huygens to his father, Constantyn Huygens
357
A
1.2
Sea clocks (sympathy of clocks). Part V
358
Appendix A2: Instantaneous phase and frequency of a signal
362
A2.1 Analytic signal and the Hubert transform
362
A2.2 Examples
363
A2.3 Numerics: practical hints and know-hows
366
A2.4 Computation of the instantaneous frequency
369
References
371
Index
405 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Pikovskij, Arkadij 1956- Rosenblum, Michael G. Kurths, Jürgen 1953- |
| author_GND | (DE-588)140665773 (DE-588)11022714X |
| author_facet | Pikovskij, Arkadij 1956- Rosenblum, Michael G. Kurths, Jürgen 1953- |
| author_role | aut aut aut |
| author_sort | Pikovskij, Arkadij 1956- |
| author_variant | a p ap m g r mg mgr j k jk |
| building | Verbundindex |
| bvnumber | BV023285613 |
| classification_rvk | UG 3900 |
| classification_tum | PHY 066 |
| ctrlnum | (OCoLC)633092376 (DE-599)BVBBV023285613 |
| discipline | Physik |
| discipline_str_mv | Physik |
| edition | 1. paperback ed. |
| format | Book |
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| id | DE-604.BV023285613 |
| illustrated | Illustrated |
| index_date | 2024-07-02T20:41:27Z |
| indexdate | 2024-07-09T21:14:58Z |
| institution | BVB |
| isbn | 9780521533522 0521592852 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016470321 |
| oclc_num | 633092376 |
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| physical | XIX, 411 S. Ill., graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | Cambridge nonlinear science series |
| series2 | Cambridge nonlinear science series |
| spelling | Pikovskij, Arkadij 1956- Verfasser (DE-588)140665773 aut Synchronization a universal concept in nonlinear sciences 1. paperback ed. Cambridge [u.a.] Cambridge Univ. Press 2007 XIX, 411 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Cambridge nonlinear science series 12 Oszillator (DE-588)4132814-0 gnd rswk-swf Synchronisierung (DE-588)4130847-5 gnd rswk-swf Synchronisierung (DE-588)4130847-5 s Oszillator (DE-588)4132814-0 s 1\p DE-604 DE-604 Rosenblum, Michael G. Verfasser aut Kurths, Jürgen 1953- Verfasser (DE-588)11022714X aut Cambridge nonlinear science series 12 (DE-604)BV004573757 12 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016470321&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Pikovskij, Arkadij 1956- Rosenblum, Michael G. Kurths, Jürgen 1953- Synchronization a universal concept in nonlinear sciences Cambridge nonlinear science series Oszillator (DE-588)4132814-0 gnd Synchronisierung (DE-588)4130847-5 gnd |
| subject_GND | (DE-588)4132814-0 (DE-588)4130847-5 |
| title | Synchronization a universal concept in nonlinear sciences |
| title_auth | Synchronization a universal concept in nonlinear sciences |
| title_exact_search | Synchronization a universal concept in nonlinear sciences |
| title_exact_search_txtP | Synchronization a universal concept in nonlinear sciences |
| title_full | Synchronization a universal concept in nonlinear sciences |
| title_fullStr | Synchronization a universal concept in nonlinear sciences |
| title_full_unstemmed | Synchronization a universal concept in nonlinear sciences |
| title_short | Synchronization |
| title_sort | synchronization a universal concept in nonlinear sciences |
| title_sub | a universal concept in nonlinear sciences |
| topic | Oszillator (DE-588)4132814-0 gnd Synchronisierung (DE-588)4130847-5 gnd |
| topic_facet | Oszillator Synchronisierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016470321&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004573757 |
| work_keys_str_mv | AT pikovskijarkadij synchronizationauniversalconceptinnonlinearsciences AT rosenblummichaelg synchronizationauniversalconceptinnonlinearsciences AT kurthsjurgen synchronizationauniversalconceptinnonlinearsciences |