Transitions of determinism and stochasticity in time ...cris/Talk/dyn_days_madrid_2013_2.pdf ·...
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Transitions of determinism and stochasticity in time-delayed complex systems with modulation Madrid, june 6th, 2013 Andrés Aragoneses , Sandro Perrone, Taciano Sorrentino, Maria Carme Torrent & Cristina Masoller Dinàmica i Òptica No Llineal i Làsers Dept. Física i Enginyeria Nuclear, Terrassa, Barcelona, Spain www.donll.upc.edu [email protected]
Transcript of Transitions of determinism and stochasticity in time ...cris/Talk/dyn_days_madrid_2013_2.pdf ·...
Transitions of determinism and stochasticity
in time-delayed complex systems with
modulation
Madrid, june 6th, 2013
Andrés Aragoneses, Sandro Perrone, Taciano Sorrentino, Maria Carme Torrent & Cristina Masoller
Dinàmica i Òptica No Llineal i Làsers Dept. Física i Enginyeria Nuclear, Terrassa, Barcelona, Spain
www.donll.upc.edu
Stochastic resonance (periodic, aperiodic) Ghost resonance (missing fundamental illusion) Entrainment, synchronization, …
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Introduction: Nonlinear oscillator with external periodic forcing
Detection of complex signals Sensors improvement Neuronal networks dynamics Human brain Animal senses
NL
Laser dynamics
+
[A. Neiman, X. Pei, W.Wojtenek, L. Wilkens, F. Moss, H. A. Braun, M. T. Huber and K. Voigt, Phys Rev. Lett., 82, (1999)] [L. Gammaitoni, P. Hänggi, P. Jung and F. Marchesoni, Rev. Mod. Phys., 70, 223 (1998)] [D. R. Chialvo, Chaos, 13, (2003)] [J. Cartwright, D.L. González, O. Piro, Phys. Rev. Lett., 82, 5389 (1999)]
1.Introduction 2. Symbolic analysis 3. Experiment & model 4. Previous results 5. Results
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GOAL: • Characterize the delayed-feedback induced complex dynamics under
the influence of an external periodic forcing, at an event-level description.
• Verify an existing model for this type of systems at this level of description.
USING:
• Symbolic time series analysis.
Goal of the work
1.Introduction 2. Symbolic analysis 3. Experiment & model 4. Previous results 5. Results
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• Aplications: fiber optics telecomunications, optical data storage, life science, material processing, sensing, ...
• Non-linear devices easily perturbed by optical feedback. • Feedback & noise (spontaneous emission) induce complex stochastic dynamics. •Stochastic resonance, ghost resonance, entrainment, synchronization, …
DIODE LASER
MIRROR TEMP CONTROLLER
PUMP CONTROLLER Time-delayed system
Introduction: Semiconductor lasers
[D. W. Sukow & D. J. Gauthier, IEEE Jour. Quan. Elec., 36, 175 (2000)] [J. M. Buldú, J. García-Ojalvo, C.R. Mirasso and M. C. Torrent, Phys. Rev. E, 66, 021106 (2002)] [C. González, J. M. Buldú, M. C. Torrent and J. García-Ojalvo, Phys. Rev. A, 76, 05824 (2007) [M. Ciszak, O. Calvo, C. Masoller, C.R. Mirasso, R. Toral, Phys. Rev. Lett., 90, 204102 (2003)]
1.Introduction 2. Symbolic analysis 3. Experiment & model 4. Previous results 5. Results
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Laser with feedback
Solitary laser
Time delay ~ 5ns <IDI> ~ 200 ns 1GHz oscilloscope
Laser output with feedback
Inter Dropout Interval = Ti
Threshold reduction
Introduction: Semiconductor lasers
1.Introduction 2. Symbolic analysis 3. Experiment & model 4. Previous results 5. Results
Ti
Experimental time trace showing the sudden dropouts. IDI = Inter Dropout Interval (Ti). Transformation of IDIs into ordinal patterns. Heart beats, epilepsy, economy, climatology, ...
D = 3 D! = 6
[C. Bandt & B. Pompe PRL, 88, 174101 (2002)] [N. Rubido, J. Tana-Alsina, M. C. Torrent J. García-Ojalvo & C. Masoller, Phys. Rev. E, 84, 026202 (2011)]
Time series analysis: Ordinal patterns
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1.Introduction 2. Symbolic analysis 3. Experiment & model 4. Previous results 5. Results
012 210
7 [A. Aragoneses, N. Rubido, J. Tiana-Alsina, M. C. Torrent & C. Masoller, Sci. Rep., 3, 1778 (2013)]
Time series analysis: Ordinal patterns
1.Introduction 2. Symbolic analysis 3. Experiment & model 4. Previous results 5. Results
D=2
D=3
(3s 95%)
01
10
01 01
01 10 10 01
10 10
8
Time series analysis: Transition probabilities
D=2
1.Introduction 2. Symbolic analysis 3. Experiment & model 4. Previous results 5. Results
10 10 01 01
01
10
01 01
01 10 10 01
10 10
9
110010101 TT
110100110 TT
D=2
Time series analysis: Transition probabilities
1.Introduction 2. Symbolic analysis 3. Experiment & model 4. Previous results 5. Results
01
10
01 01
01 10 10 01
10 10
10
11010*
0110*
1001*
0101* TTTT
D=2
Time series analysis: Transition probabilities
TP
s*
1.Introduction 2. Symbolic analysis 3. Experiment & model 4. Previous results 5. Results
- Ordinal patterns analysis is a useful tool to dintinguish signatures of determinism and stochasticity in spiking complex systems. - Transition probabilities of D=2 show that the system has memory of up to 4 consecutive events.
1.Introduction 2. Symbolic analysis 3. Experiment & model 4. Previous results 5. Results
Time series analysis: Ordinal patterns
E(t) slowly varying complex electric field N(t) carrier density a linewidth enhancement factor e saturation coeficient h feedback strength k field decay rate t time delay w0 angular frequency solitary m normalized pump current inverse carrier lifetime
)sin(
)(
)()()(1),(1)(
00
2
20
tba
EgNtN
ttEetEENgiktE
N
sp
i
wm
m
tha tw
N14
1
00
0
0
1
1
10
1
)1.0:01.0:01.0·(
1.1:01.0:98.0
11.1
5
300
]60:10:10[
01.0
4
ns
ns
ab
a
ns
nsk
ns
sp
N
tw
t
h
e
a
Feedback term Noise term
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2
2
1),(
E
NENg
e optical gain
External periodic forcing
[R. Lang & K. Kobayashi, IEEE Jour. Quan. Elec., 3, 347 (1980)]
The Lang-Kobayashi model
1.Introduction 2. Symbolic analysis 3. Experiment & model 4. Previous results 5. Results
Time delay ~ 5ns <IDI> ~ 200 ns 8% threshold reduction
Time delay ~ 25ns <IDI> ~ 2000 ns 10% threshold reduction
nm
II th
660
·03.1
nm
II th
1550
·12.1
13
Experimental setup
1.Introduction 2. Symbolic analysis 3. Experiment & model 4. Previous results 5. Results
Events histograms
1.Introduction 2. Symbolic analysis 3. Experiment & model 4. Previous results 5. Results
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Histograms of [event(i+1)-event(i)]
1.Introduction 2. Symbolic analysis 3. Experiment & model 4. Previous results 5. Results
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Return maps
1.Introduction 2. Symbolic analysis 3. Experiment & model 4. Previous results 5. Results
Results: Ordinal patterns (experiments and simulations)
17 reductionthreshold
mAI
II
MHzf
th
th
%8
38
·03.1
17
110
01.1
15
ns
MHzf
h
m
1.Introduction 2. Symbolic analysis 3. Experiment & model 4. Previous results 5. Results
D=2
D=3
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Results: Transition probabilities (experiments & simulations)
110
01.1
15
ns
MHzf
h
m
reductionthreshold
mAI
II
MHzf
th
th
%8
38
·03.1
17
1.Introduction 2. Symbolic analysis 3. Experiment & model 4. Previous results 5. Results
D=2
19 8,000-19,000 IDIs 74,000-207,000 IDIs
reductionthreshold
mAI
II
MHzf
th
th
%10
2.12
·12.1
2
Results: Free space laser vesus optical fiber laser
reductionthreshold
mAI
II
MHzf
th
th
%8
38
·03.1
17
1.Introduction 2. Symbolic analysis 3. Experiment & model 4. Previous results 5. Results
D=2
D=3
- Lang & Kobayashi model describes sucessfully the dynamics found in experiments at the event level of description of the LFFs. - A structure in the OPs and TPs is found for up to 4 consecutive events.
- A clustering of the ordinal patterns is found for a wide range of conditions and both, for experiments and simulations.
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Conclusions
Transitions of determinism and stochasticity
in time-delayed complex systems with
modulation
Madrid, june 6th, 2013
Andrés Aragoneses, Sandro Perrone, Taciano Sorrentino, Maria Carme Torrent & Cristina Masoller
Dinàmica i Òptica No Llineal i Làsers Dept. Física i Enginyeria Nuclear, Terrassa, Barcelona, Spain
www.donll.upc.edu
Thank you for your attention
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Results: Effect of frequency (Ordinal patterns)
reductionthreshold
mAI
II
MHzf
th
th
%8
38
·03.1
17
110
01.1
15
ns
MHzf
h
m
1.Introduction 2. Symbolic analysis 3. Experiment & model 4. Previous results 5. Results
D=2
D=3
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Results: Effect of frequency (transition probabilities)
nm
reductionthreshold
II th
660
%8
03.1
110
01.1
nsh
m
1.Introduction 2. Symbolic analysis 3. Experiment & model 4. Previous results 5. Results
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Introduction: Semiconductor lasers
1.Introduction 2. Symbolic analysis 3. Experiment & model 4. Previous results 5. Results
