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Tables of Contents for Space-Time Chaos
Chapter/Section Title
Page #
Page Count
Preface
v
I Analysis and Characterization of chaotic, complex and space extended systems
1
168
Non-Stationarity as an Embedding Problem
3
16
Michael Small
Dejin Yu
Robert G. Harrison
Introduction
3
1
Modelling
4
4
Reconstruction
4
1
Radial Basis Modelling
5
1
Minimum Description Length
6
1
Cylindrical Basis Models
7
1
Embedding Time
7
1
Applications
8
9
Nonstationary Simulations
8
2
Chaos in Computational Simulations
10
2
Vibrating Strings
12
1
Bifurcating Babies
12
3
Fibrillation
15
2
Conclusion
17
2
Nonlinear Dynamics and Time Series Analysis: A Basic Introduction
19
10
E. J. Kostelich
Introduction
19
1
The embedding problem
20
4
Noise reduction in chaotic data
24
2
Other resources
26
3
Fixed Point Analysis: Dynamics of Non-Stationary Spatiotemporal Signals
29
16
A. Hutt
F. Kruggel
Introduction
29
1
A simulated dataset: Kuppers-Lortz instability
30
2
Fixed Point Clustering
32
4
The clustering algorithm
33
1
Results of clustering
33
3
Spatiotemporal Modeling
36
4
Fixed Point Analysis (FPA)
40
1
Summary
41
1
Acknowledgments
42
3
Complex-Valued Second Difference as a Measure of Stabilization of Complex Dissipative Statistical Systems: Girko Ensemble
45
8
Maciej. M. Duras
Summary
45
1
Introduction
45
2
Second Difference Distributions
47
2
Conclusions
49
4
Study of a C-Integrable Partial Differential Equation
53
8
A. Di Garbo
S. Chillemi
L. Fronzoni
Introduction
53
1
Properties of the PDE
54
1
Explicit solutions
55
3
Conclusions
58
3
Wave Patterns in Coupled Map Lattices
61
18
Pedro Goncalves Lind
Joao Alexandre Medina Cortereal
Jason Alfredo Carlson Gallas
Introduction
61
2
Coupled Map Lattices
63
1
The Five Classes of Time-evolution
64
6
Algorithm for automatic classification of time-evolutions
70
3
Definition of the period τ
70
2
Definition of d
72
1
Dynamical Characteristics of the Five Classes
73
1
Conclusions
74
5
Chaos in Air Bubble Formation
79
8
A. Tufaile
J.C. Sartorelli
Introduction
79
1
Experimental apparatus
79
1
Bifurcation
80
2
Anti-bubbles
82
1
Sound wave
83
1
Conclusions
84
3
Patterns in a Nonlinear Optical System
87
18
F.T. Arecchi
P.L Ramazza
Introduction
87
4
The Liquid Crystal Light valve with optical feedback: principles of operation and conditions for pattern formation
91
5
Effects of nonlocal interactions: rotation
96
3
Effects of nonlocal interactions: translation
99
3
Conclusions
102
3
Bifurcation Behavior of a Superlattice Model
105
8
J. Galan
M. Moscoso
L. L. Bonilla
Introduction
105
1
Model
105
1
Results and discussion
106
5
Conclusions
111
2
Delayed Dynamical Systems with Variable Delay
113
10
S. Madruga
S. Boccaletti
M.A. Matias
Introduction
113
2
Variable delay
115
6
Dynamical behavior of VDS
117
1
Results for sinusoidal modulation
118
1
Results for triangular modulation
119
2
Conclusions and Future Goals
121
2
Stability of Hexagonal Patterns in a Generalized Swift-Hohenberg Equation
123
14
B. Pena
C. Perez-Garcia
B. Echebarria
Introduction
123
1
Model equation
124
2
Linear analysis
125
1
Center Manifold Reduction to a pattern with hexagonal symmetry
126
2
Multiple scale analysis for a hexagonal pattern
128
2
Stability diagrams
130
5
Amplitude instabilities
131
1
Phase equations of a hexagonal pattern
132
2
Numerical simulations
134
1
Conclusions
135
2
Rayleigh-Benard Convective Instabilities in Nematic Liquid Crystals
137
20
Jesus Salan
Italo Bove
Introduction
137
3
Planar Nematics and horizontal magnetic field
140
5
Thresholds
140
5
No linear properties
145
1
Homeotropic NLC under external magnetic fields heating from below
145
4
Threshold
145
3
Non linear effects
148
1
Homeotropic NLC under external magnetic fields heating from above
149
8
Introduction
149
1
Field H parallel to director n
150
2
Field H perpendicular to director n
152
5
Topological Analysis in a Dripping Faucet Experiment
157
12
M.B. Reyes
J.C. Sartorelli
Introduction
157
1
Experimental Apparatus
157
2
Results and discussion
159
1
Partition of the phase space
160
4
Topological Characterization
164
5
II Control and Synchronization of chaos and space time chaos
169
124
The Breakdown of Synchronization and Shadowing in Coupled Chaotic Systems: Analysis Via the Subsystem Decomposition
171
20
Ernest Barreto
Paul So
Introduction
171
1
Defining UPO Subsystems
172
1
Desynchronization Beyond Generalized Synchrony
173
8
Introduction
173
2
Evolution of the Attractor
175
2
Subsystem Analysis
177
1
Measuring the decoherence transition from trajectory data
178
1
Noise
179
1
Conclusion
180
1
The Breakdown of Shadowing
181
7
Introduction
181
1
Subsystem Analysis
181
3
Mechanisms for the Development of UDV
184
1
Breakdown of Shadowing is Common in Coupled Systems
185
1
Quantifying UDV and Shadowing Times
186
2
Conclusion
188
3
Anticipating Chaotic Synchronization an --- Overview
191
20
H. U. Voss
Introduction
191
1
Time-delayed feedback systems
192
2
Coupled time-delayed feedback systems
194
2
Time-delayed dissipative coupling
196
4
Drive systems without a memory
200
3
Systems without memory
203
1
Discrete and spatiotemporal dynamics
203
2
Overview and Discussion
205
6
Phase Synchronization in Chaotic Convection
211
12
D. Maza
A. Vallone
H. Mancini
S. Boccaletti
Introduction
211
1
Experimental Setup
212
2
From Chaotic Oscillations to Phase Synchronization
214
5
Conclusion
219
4
A Simple Use of the Diffusion Approximation for Treating Roundoff-Induced Problems in Coupled Maps with an Invariant Subset
223
10
Giovanni Santoboni
Rua Murray
Steven R. Bishop
Introduction
223
2
An analytically solvable example
225
3
Analytical estimates
225
1
Numerical results
226
1
The role of the integration parameters
227
1
Diffusion approximation
228
4
Comments
232
1
Out-of-Phase vs In-Phase Synchronization of Two Parametrically Excited Pendula
233
18
Ana Guedes de Oliveira
Winston S. Garira
Steve R. Bishop
Introduction and Motivation
233
1
Single Parametric Excited Pendulum
233
2
Coupled Parametric Excited Pendula
235
11
Synchronization: Numerical Simulations
239
7
Concluding Remarks and Future research
246
5
Experiments on Chaos Control in Lasers
251
22
R. Meucci
F.T. Arecchi
Introduction
251
1
The Physical System: a CO2 laser with feedback
252
3
Stabilization of an Unstable Fixed Point
255
7
Control of chaos in a delayed high-dimensional system
262
6
Conclusions
268
5
Communication with Chaos: Reconstructing Information-Carrying Signals
273
20
I. P. Marino
D. L. Valladares
C. Grebogi
S. Boccaletti
E. Rosa Jr.
Introduction
273
2
Encoding technique
275
5
Dropout reconstruction
280
8
First Reconstruction Method (FRM)
282
4
Second Reconstruction Method (SRM)
286
2
Multiplexing
288
1
Conclusions
289
4
List of Participants
293