The logistic map and the route to chaos: from the beginnings to modern applications
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Heidelberg ; New York
Springer
2006
|
| Schriftenreihe: | Springer complexity
Understanding complex systems |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturangaben |
| Beschreibung: | XX, 411 S. Ill., graph. Darst. 24 cm |
| ISBN: | 9783540283669 3540283668 |
Internformat
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| 020 | |a 3540283668 |c Pp. : EUR 106.95 (freier Pr.), ca. sfr 169.00 (freier Pr.) |9 3-540-28366-8 | ||
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| 245 | 1 | 0 | |a The logistic map and the route to chaos |b from the beginnings to modern applications |c M. Ausloos ; M. Dirickx (ed.) |
| 264 | 1 | |a Berlin ; Heidelberg ; New York |b Springer |c 2006 | |
| 300 | |a XX, 411 S. |b Ill., graph. Darst. |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Springer complexity | |
| 490 | 0 | |a Understanding complex systems | |
| 500 | |a Literaturangaben | ||
| 600 | 1 | 4 | |a Verhulst, P.-F <1804-1849> - (Pierre François) |
| 600 | 1 | 4 | |a Verhulst, P.-F <1804-1849> |q (Pierre François) |
| 650 | 4 | |a Chaos | |
| 650 | 4 | |a Chaotic behavior in systems | |
| 650 | 0 | 7 | |a Chaostheorie |0 (DE-588)4009754-7 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4143413-4 |a Aufsatzsammlung |2 gnd-content | |
| 689 | 0 | 0 | |a Chaostheorie |0 (DE-588)4009754-7 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Ausloos, Marcel |e Sonstige |4 oth | |
| 856 | 4 | 2 | |m DNB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014683370&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-014683370 | ||
Datensatz im Suchindex
| _version_ | 1804135187615842304 |
|---|---|
| adam_text | CONTENTS
PART
I
GENERAL
AND
HISTORICAL
INTRODUCTION
CHAOTIC
GROWTH
WITH
THE
LOGISTIC
MODEL
OF
P.-F.
VERHULST
H.
PASTIJN
.....................................................
3
1
P.-F.
VERHULST
AND
THE
ROYAL
MILITARY
ACADEMY
INBRUSSELS
.................................................
3
2
THE
EXPONENTIAL
GROWTH
PROCESS..............................
5
3
LIMITED
GROWTH
MODELS
......................................
6
4
THE
LOGISTIC
GROWTH
PROCESS
.................................
7
5
ATTRACTORS
FOR
THE
DISCRETE
LOGISTIC
MODEL
......................
9
6
CONCLUSION
.................................................
10
REFERENCES
.....................................................
10
PIERRE-FRAN¸COIS
VERHULST S
FINAL
TRIUMPH
J.
KINT,
D.
CONSTALES,
A.
VANDERBAUWHEDE
.........................
13
1
HISLIFE....................................................
13
2
HIS
WORK
IN
THE
FIELD
OF
POPULATION
GROWTH
....................
17
3
THE
LOGISTIC
FUNCTION
AFTER
1849..............................
19
4
VERHULST SPRINCIPLEANDCHAOSTHEORY.........................
22
5
LOGISTIC
FRACTAL
OF
VERHULST
...................................
24
6
CONCLUSION
.................................................
26
REFERENCES
.....................................................
27
LIMITS
TO
SUCCESS.
THE
IRON
LAW
OF
VERHULST
P.L.
KUNSCH
...................................................
29
1
INTRODUCTION
................................................
29
2
THE
LOGISTIC
EQUATION,
A
PROTOTYPE
OFSYSTEMSTHINKING.........................................
30
3
ARCHETYPES
.................................................
34
4
MODELLING
A
BUBBLE
ON
THE
STOCK
MARKET
.......................
40
5
CONCLUSIONS.................................................
49
REFERENCES
.....................................................
50
X
CONTENTS
RECURRENT
GENERATION
OF
VERHULST
CHAOS
MAPS
AT
ANY
ORDER
AND
THEIR
STABILIZATION
DIAGRAM
BY
ANTICIPATIVE
CONTROL
D.M.
DUBOIS
...................................................
53
1
INTRODUCTION
................................................
53
2
ANALYTICAL
SOLUTION
OF
CHAOS
MAPS
............................
54
3
THE
VERHULST
INCURSIVE
MAP
IS
THE
CORRECT
DISCRETE
VERHULST
EQUATION.......................
57
4
INCURSIVE
CONTROL
FOR
STABILIZING
CHAOS
MAPS
...................
59
5
RECURRENT
GENERATION
OF
CHAOS
MAPS
AT
ANY
ORDER
..............
64
6
CONCLUSIONS.................................................
74
REFERENCES
.....................................................
75
COHERENCE
IN
COMPLEX
NETWORKS
OF
OSCILLATORS
P.G.
LIND,
J.A.C.
GALLAS,
H.J.
HERRMANN
.........................
77
1
THE
INTERPLAY
BETWEEN
DYNAMICS
AND
TOPOLOGY
.................
77
2
GENERAL
APPROACH
TO
ANALYSE
COHERENT
STATES
..................
81
3
SCALE-FREE
NETWORKS
OF
COUPLED
LOGISTIC
MAPS:
ANEXAMPLE................................................
83
4
DISCUSSIONANDCONCLUSIONS...................................
95
REFERENCES
.....................................................
96
GROWTH
OF
RANDOM
SEQUENCES
K.
AUSTIN,
G.J.
RODGERS
.........................................
99
1
INTRODUCTION
................................................
99
2
SEQUENCES
WITH
RANDOM
ELEMENTS
CHOSEN
FROM
A
PROBABILITY
DISTRIBUTION
...............................
102
3
RANDOM
SEQUENCES
WITH
MULTIPLICATIVE
CONSTANTS
...............
106
4
DISCUSSION..................................................111
REFERENCES
.....................................................
113
PART
II
LIFE
RELEVANT
PHYSICS
LOGISTIC
POPULATION
GROWTH
AND
BEYOND:
THE
INFLUENCE
OF
ADVECTION
AND
NONLOCAL
EFFECTS
E.
HERN´ANDEZ-GARC´YY
A
,C
.L´
OPEZ
...................................
117
1
INTRODUCTION
................................................
117
2
PLANKTON
DYNAMICS
DRIVEN
BYANENVIRONMENTALOPENFLOW
..............................118
3
NONLOCAL
LOGISTIC
GROWTH
....................................
122
4
SUMMARY...................................................
128
REFERENCES
.....................................................
129
CONTENTS
XI
PREDATOR-PREY
ENCOUNTERS
STUDIED
AS
RELATIVE
PARTICLE
DIFFUSION
J.
MANN,
S.
OTT,
H.L.
P´ECSELI,
J.
TRULSEN
..........................
131
1
INTRODUCTION
................................................
131
2
EXPERIMENTALSET-UP.........................................132
3
PARTICLE
FLUX
INTO
A
MOVING
SPHERE
............................
136
4
ANALYTICALRESULTS...........................................137
5
CONCLUSIONS.................................................143
REFERENCES
.....................................................
145
EXTINCTION
DYNAMICS
IN
LOTKA-VOLTERRA
ECOSYSTEMS
ON
EVOLVING
NETWORKS
A.
LIPOWSKI,
M.
DROZ
............................................
147
1
INTRODUCTION
................................................
147
2
MODEL
AND
NUMERICAL
CALCULATIONS
............................
150
3
RESULTS.....................................................151
4
CONCLUSIONS.................................................157
REFERENCES
.....................................................
158
EXACT
LAW
OF
LIVE
NATURE
MARK
YA.
AZBEL
................................................
161
1
MOTIVATION
AND
APPROACH
....................................
161
2
UNIVERSALITY
LAW:
DERIVATION..................................
163
3
RESULTS.....................................................165
4
DISCUSSIONANDCONCLUSIONS...................................167
5
OUTSTANDINGPROBLEMS
.......................................170
REFERENCES
.....................................................
172
MANIFESTATION
OF
CHAOS
IN
REAL
COMPLEX
SYSTEMS:
CASE
OF
PARKINSON S
DISEASE
R.M.
YULMETYEV,
S.A.
DEMIN,
P.
H¨ANGGI
...........................
175
1
INTRODUCTION
................................................
175
2
THE
STATISTICAL
THEORY
OF
DISCRETE
NON-MARKOV
RANDOM
PROCESSES.
NON-MARKOVITY
PARAMETER
AND
ITS
FREQUENCY
SPECTRUM
..................................
178
3
THE
UNIVERSAL
PROPERTY
OF
INFORMATIONAL
MANIFESTATION
OF
CHAOTICITY
IN
COMPLEX
SYSTEMS
...............................
180
4
THE
QUANTITATIVE
FACTOR
OF
QUALITY
OF
A
TREATMENT
..............
181
5
EXPERIMENTALDATA
..........................................183
6
RESULTS.....................................................185
7
CONCLUSIONS.................................................193
REFERENCES
.....................................................
196
XII
CONTENTS
MONTE
CARLO
SIMULATIONS
OF
AGEING
AND
SPECIATION
S.
MOSS
DE
OLIVEIRA,
D.
STAUFFER
..................................
197
1
INTRODUCTION
................................................
197
2
THE
PENNA
MODEL
...........................................
198
3
SYMPATRIC
SPECIATION
........................................
210
REFERENCES
.....................................................
217
PART
III
ECONOPHYSICS
INFLUENCE
OF
INFORMATION
FLOW
IN
THE
FORMATION
OF
ECONOMIC
CYCLES
J.
MISKIEWICZ,
M.
AUSLOOS
........................................
223
1
INTRODUCTION
................................................
223
2
ACPMODEL.................................................224
3
RESULTS.....................................................225
4
CONCLUSIONS.................................................235
5
ACKNOWLEDGEMENT
...........................................238
REFERENCES
.....................................................
238
LOGISTIC
FUNCTION
IN
LARGE
FINANCIAL
CRASHES
G.
ROTUNDO
....................................................
239
1
INTRODUCTION
................................................
239
2
LARGEFINANCIALCRASHESMODELS...............................240
3
THE
LOGISTIC
FUNCTION........................................
242
4
NUMERICALRESULTS...........................................243
5
BAYESIANANALYSIS
...........................................255
6
CONCLUSIONS.................................................257
REFERENCES
.....................................................
257
AGENT
BASED
APPROACHES
TO
INCOME
DISTRIBUTIONS
AND
THE
IMPACT
OF
MEMORY
P.
REPETOWICZ,
P.
RICHMOND,
S.
HUTZLER,
E.
NI
DHUINN
..............
259
1
INTRODUCTION
................................................
259
2
KINETICS
OF
WEALTH
DISTRIBUTIONS
..............................
261
3
LACKOFMEMORYANDEQUALSAVINGS............................264
4
THREE-AGENT
EXCHANGE
PROCESSES
..............................
265
5
COMPARISON
OF
THE
MODEL
TO
EMPIRICAL
DATA
....................
267
6
PRESENCE
OF
MEMORY
AND
RANDOM
SAVINGS
......................
267
7
CONCLUSIONS.................................................270
REFERENCES
.....................................................
271
CONTENTS
XIII
PART
IV
CONDENSED
MATTER
AGGLOMERATION/AGGREGATION
AND
CHAOTIC
BEHAVIOUR
IN
D
-DIMENSIONAL
SPATIO-TEMPORAL
MATTER
REARRANGEMENTS
NUMBER-THEORETIC
ASPECTS
A.
GADOMSKI,
M.
AUSLOOS
........................................
275
1
INTRODUCTION
................................................
275
2
AGGLOMERATION
VS
AGGREGATION
OF
MATTER
-
A
MODEL
DESCRIPTION
...
277
3
QUALITATIVE
SIGNATURES
OF
CHAOS
IN
MATTER-AGGLOMERATING
SYSTEM
.
287
4
SOME
QUANTITATIVE
MEASURES
OF
CHAOS
SIGNATURES
IN
MATTER-AGGLOMERATING
SYSTEM..............................
287
5
NUMBER-THEORETICMEASURESOFSPATIALANDTEMPORALIRREGULARITIES
IN
AGGREGATION-AGGLOMERATING
SYSTEMS.........................
289
6
CHAOS
IN
AN
INFINITE-DIMENSIONAL
AGGLOMERATING
AND/OR
AGGREGATING
SYSTEM
.........................................
291
7
CONCLUDINGADDRESS
.........................................292
REFERENCES
.....................................................
293
A
CHAOS
AND
FRACTAL
DYNAMIC
APPROACH
TO
THE
FRACTURE
MECHANICS
L.M.
ALVES,
R.F.M.
LOBO
........................................
295
1
INTRODUCTION
................................................
295
2
THEORETICAL
DEVELOPMENT
OF
A
CHAOTIC
MODEL
TO
DYNAMIC
FRACTURE.........................................
297
3
RESULTS.....................................................309
4
DISCUSSION..................................................313
5
SUMMARY
AND
CONCLUSIONS....................................
313
REFERENCES
.....................................................
315
NONLINEAR
DYNAMICS
AND
FRACTAL
AVALANCHES
IN
A
PILE
OF
RICE
R.J.
WIJNGAARDEN,
K.A.
LYYORINCZ,
C.M.
AEGERTER
....................
317
1
INTRODUCTION
................................................
317
2
EXPERIMENT:ABIGRICEPILE..................................318
3
THEROUGHSURFACEOFTHEPILE
................................320
4
AVALANCHES
ON
THE
RICE
PILE
..................................
322
5
RELATION
BETWEEN
AVALANCHES
AND
SURFACE
......................
324
6
AVALANCHES
AS
SPATIOTEMPORAL
FRACTALS
.........................
326
7
HOW
TO
PREVENT
AVALANCHES...................................
328
8
CONCLUSIONS.................................................333
REFERENCES
.....................................................
334
XIV
CONTENTS
PART
V
MISCELLANEOUS
A
RECENT
APPRECIATION
OF
THE
SINGULAR
DYNAMICS
AT
THE
EDGE
OF
CHAOS
E.
MAYORAL,
A.
ROBLEDO
..........................................
339
1
INTRODUCTION
................................................
339
2
CRITICAL
ATTRACTORS
IN
THE
LOGISTIC
MAP.........................
341
3
MORI S
Q
-PHASE
TRANSITIONS
IN
THE
LOGISTIC
MAP..................
342
4
TSALLIS
DYNAMICS
AT
THE
EDGE
OF
CHAOS.........................
343
5
A
FAMILY
OF
Q
-PHASE
TRANSITIONS
AT
THE
EDGE
OF
CHAOS
...........
346
6
NOISY
DYNAMICS
AT
THE
EDGE
OF
CHAOS..........................
348
7
ANALOGY
WITH
GLASSY
DYNAMICS
...............................
350
8
CONCLUDINGREMARKS.........................................352
REFERENCES
.....................................................
353
QUANTUM
CHAOS
VERSUS
CLASSICAL
CHAOS:
WHY
IS
QUANTUM
CHAOS
WEAKER?
H.
KR¨OGER,
J.-F.
LAPRISE,
G.
MELKONYAN,
R.
ZOMORRODI
..............
355
1
INTRODUCTION
................................................
355
2
CASES
WHERE
QUANTUM
CHAOS
WAS
FOUND
TOBEWEAKER...............................................356
3
UNIFORM
DESCRIPTION
OF
CHAOS.................................
358
4
RENORMALISATION
FLOW
OF
PARAMETERS
OF
THE
QUANTUM
ACTION
......................................
362
5
INTERPRETATION...............................................
366
REFERENCES
.....................................................
367
ON
THE
PREDICTION
OF
CHAOS
IN
THE
RESTRICTED
THREE-BODY
PROBLEM
HOUMAN
SAFAAI,
MOHAMMAD
HASAN
GHAFFARI
SAADAT
.................
369
1
INTRODUCTION
................................................
369
2
THE
RELATIONSHIP
BETWEEN
MECHANICS
AND
RIEMANNIAN
GEOMETRY
..
370
3
NUMERICAL
COMPUTATION
FOR
RESTRICTED
THREE-BODY
PROBLEM
......
376
4
CONCLUSION
.................................................382
REFERENCES
.....................................................
383
ORDER
AND
CHAOS
IN
SOME
HAMILTONIAN
SYSTEMS
OF
INTEREST
IN
PLASMA
PHYSICS
D.
CONSTANTINESCU,
B.
WEYSSOW
..................................
385
1
INTRODUCTION
................................................
385
2
THE
MATHEMATICAL
MODELS....................................
386
3
DEFINITIONS
AND
BASIC
RESULTS
.................................
389
4
TRANSPORTBARRIERS...........................................394
CONTENTS
XV
5
RECONNECTION
AND
TRANSPORT
BARRIERS
..........................
400
6
CONCLUSIONS.................................................402
REFERENCES
.....................................................
404
INDEX
.........................................................407
|
| adam_txt |
CONTENTS
PART
I
GENERAL
AND
HISTORICAL
INTRODUCTION
CHAOTIC
GROWTH
WITH
THE
LOGISTIC
MODEL
OF
P.-F.
VERHULST
H.
PASTIJN
.
3
1
P.-F.
VERHULST
AND
THE
ROYAL
MILITARY
ACADEMY
INBRUSSELS
.
3
2
THE
EXPONENTIAL
GROWTH
PROCESS.
5
3
LIMITED
GROWTH
MODELS
.
6
4
THE
LOGISTIC
GROWTH
PROCESS
.
7
5
ATTRACTORS
FOR
THE
DISCRETE
LOGISTIC
MODEL
.
9
6
CONCLUSION
.
10
REFERENCES
.
10
PIERRE-FRAN¸COIS
VERHULST'S
FINAL
TRIUMPH
J.
KINT,
D.
CONSTALES,
A.
VANDERBAUWHEDE
.
13
1
HISLIFE.
13
2
HIS
WORK
IN
THE
FIELD
OF
POPULATION
GROWTH
.
17
3
THE
LOGISTIC
FUNCTION
AFTER
1849.
19
4
VERHULST'SPRINCIPLEANDCHAOSTHEORY.
22
5
LOGISTIC
FRACTAL
OF
VERHULST
.
24
6
CONCLUSION
.
26
REFERENCES
.
27
LIMITS
TO
SUCCESS.
THE
IRON
LAW
OF
VERHULST
P.L.
KUNSCH
.
29
1
INTRODUCTION
.
29
2
THE
LOGISTIC
EQUATION,
A
PROTOTYPE
OFSYSTEMSTHINKING.
30
3
ARCHETYPES
.
34
4
MODELLING
A
BUBBLE
ON
THE
STOCK
MARKET
.
40
5
CONCLUSIONS.
49
REFERENCES
.
50
X
CONTENTS
RECURRENT
GENERATION
OF
VERHULST
CHAOS
MAPS
AT
ANY
ORDER
AND
THEIR
STABILIZATION
DIAGRAM
BY
ANTICIPATIVE
CONTROL
D.M.
DUBOIS
.
53
1
INTRODUCTION
.
53
2
ANALYTICAL
SOLUTION
OF
CHAOS
MAPS
.
54
3
THE
VERHULST
INCURSIVE
MAP
IS
THE
CORRECT
DISCRETE
VERHULST
EQUATION.
57
4
INCURSIVE
CONTROL
FOR
STABILIZING
CHAOS
MAPS
.
59
5
RECURRENT
GENERATION
OF
CHAOS
MAPS
AT
ANY
ORDER
.
64
6
CONCLUSIONS.
74
REFERENCES
.
75
COHERENCE
IN
COMPLEX
NETWORKS
OF
OSCILLATORS
P.G.
LIND,
J.A.C.
GALLAS,
H.J.
HERRMANN
.
77
1
THE
INTERPLAY
BETWEEN
DYNAMICS
AND
TOPOLOGY
.
77
2
GENERAL
APPROACH
TO
ANALYSE
COHERENT
STATES
.
81
3
SCALE-FREE
NETWORKS
OF
COUPLED
LOGISTIC
MAPS:
ANEXAMPLE.
83
4
DISCUSSIONANDCONCLUSIONS.
95
REFERENCES
.
96
GROWTH
OF
RANDOM
SEQUENCES
K.
AUSTIN,
G.J.
RODGERS
.
99
1
INTRODUCTION
.
99
2
SEQUENCES
WITH
RANDOM
ELEMENTS
CHOSEN
FROM
A
PROBABILITY
DISTRIBUTION
.
102
3
RANDOM
SEQUENCES
WITH
MULTIPLICATIVE
CONSTANTS
.
106
4
DISCUSSION.111
REFERENCES
.
113
PART
II
LIFE
RELEVANT
PHYSICS
LOGISTIC
POPULATION
GROWTH
AND
BEYOND:
THE
INFLUENCE
OF
ADVECTION
AND
NONLOCAL
EFFECTS
E.
HERN´ANDEZ-GARC´YY
A
,C
.L´
OPEZ
.
117
1
INTRODUCTION
.
117
2
PLANKTON
DYNAMICS
DRIVEN
BYANENVIRONMENTALOPENFLOW
.118
3
NONLOCAL
LOGISTIC
GROWTH
.
122
4
SUMMARY.
128
REFERENCES
.
129
CONTENTS
XI
PREDATOR-PREY
ENCOUNTERS
STUDIED
AS
RELATIVE
PARTICLE
DIFFUSION
J.
MANN,
S.
OTT,
H.L.
P´ECSELI,
J.
TRULSEN
.
131
1
INTRODUCTION
.
131
2
EXPERIMENTALSET-UP.132
3
PARTICLE
FLUX
INTO
A
MOVING
SPHERE
.
136
4
ANALYTICALRESULTS.137
5
CONCLUSIONS.143
REFERENCES
.
145
EXTINCTION
DYNAMICS
IN
LOTKA-VOLTERRA
ECOSYSTEMS
ON
EVOLVING
NETWORKS
A.
LIPOWSKI,
M.
DROZ
.
147
1
INTRODUCTION
.
147
2
MODEL
AND
NUMERICAL
CALCULATIONS
.
150
3
RESULTS.151
4
CONCLUSIONS.157
REFERENCES
.
158
EXACT
LAW
OF
LIVE
NATURE
MARK
YA.
AZBEL'
.
161
1
MOTIVATION
AND
APPROACH
.
161
2
UNIVERSALITY
LAW:
DERIVATION.
163
3
RESULTS.165
4
DISCUSSIONANDCONCLUSIONS.167
5
OUTSTANDINGPROBLEMS
.170
REFERENCES
.
172
MANIFESTATION
OF
CHAOS
IN
REAL
COMPLEX
SYSTEMS:
CASE
OF
PARKINSON'S
DISEASE
R.M.
YULMETYEV,
S.A.
DEMIN,
P.
H¨ANGGI
.
175
1
INTRODUCTION
.
175
2
THE
STATISTICAL
THEORY
OF
DISCRETE
NON-MARKOV
RANDOM
PROCESSES.
NON-MARKOVITY
PARAMETER
AND
ITS
FREQUENCY
SPECTRUM
.
178
3
THE
UNIVERSAL
PROPERTY
OF
INFORMATIONAL
MANIFESTATION
OF
CHAOTICITY
IN
COMPLEX
SYSTEMS
.
180
4
THE
QUANTITATIVE
FACTOR
OF
QUALITY
OF
A
TREATMENT
.
181
5
EXPERIMENTALDATA
.183
6
RESULTS.185
7
CONCLUSIONS.193
REFERENCES
.
196
XII
CONTENTS
MONTE
CARLO
SIMULATIONS
OF
AGEING
AND
SPECIATION
S.
MOSS
DE
OLIVEIRA,
D.
STAUFFER
.
197
1
INTRODUCTION
.
197
2
THE
PENNA
MODEL
.
198
3
SYMPATRIC
SPECIATION
.
210
REFERENCES
.
217
PART
III
ECONOPHYSICS
INFLUENCE
OF
INFORMATION
FLOW
IN
THE
FORMATION
OF
ECONOMIC
CYCLES
J.
MISKIEWICZ,
M.
AUSLOOS
.
223
1
INTRODUCTION
.
223
2
ACPMODEL.224
3
RESULTS.225
4
CONCLUSIONS.235
5
ACKNOWLEDGEMENT
.238
REFERENCES
.
238
LOGISTIC
FUNCTION
IN
LARGE
FINANCIAL
CRASHES
G.
ROTUNDO
.
239
1
INTRODUCTION
.
239
2
LARGEFINANCIALCRASHESMODELS.240
3
THE
LOGISTIC
FUNCTION.
242
4
NUMERICALRESULTS.243
5
BAYESIANANALYSIS
.255
6
CONCLUSIONS.257
REFERENCES
.
257
AGENT
BASED
APPROACHES
TO
INCOME
DISTRIBUTIONS
AND
THE
IMPACT
OF
MEMORY
P.
REPETOWICZ,
P.
RICHMOND,
S.
HUTZLER,
E.
NI
DHUINN
.
259
1
INTRODUCTION
.
259
2
KINETICS
OF
WEALTH
DISTRIBUTIONS
.
261
3
LACKOFMEMORYANDEQUALSAVINGS.264
4
THREE-AGENT
EXCHANGE
PROCESSES
.
265
5
COMPARISON
OF
THE
MODEL
TO
EMPIRICAL
DATA
.
267
6
PRESENCE
OF
MEMORY
AND
RANDOM
SAVINGS
.
267
7
CONCLUSIONS.270
REFERENCES
.
271
CONTENTS
XIII
PART
IV
CONDENSED
MATTER
AGGLOMERATION/AGGREGATION
AND
CHAOTIC
BEHAVIOUR
IN
D
-DIMENSIONAL
SPATIO-TEMPORAL
MATTER
REARRANGEMENTS
NUMBER-THEORETIC
ASPECTS
A.
GADOMSKI,
M.
AUSLOOS
.
275
1
INTRODUCTION
.
275
2
AGGLOMERATION
VS
AGGREGATION
OF
MATTER
-
A
MODEL
DESCRIPTION
.
277
3
QUALITATIVE
SIGNATURES
OF
CHAOS
IN
MATTER-AGGLOMERATING
SYSTEM
.
287
4
SOME
QUANTITATIVE
MEASURES
OF
CHAOS
SIGNATURES
IN
MATTER-AGGLOMERATING
SYSTEM.
287
5
NUMBER-THEORETICMEASURESOFSPATIALANDTEMPORALIRREGULARITIES
IN
AGGREGATION-AGGLOMERATING
SYSTEMS.
289
6
CHAOS
IN
AN
INFINITE-DIMENSIONAL
AGGLOMERATING
AND/OR
AGGREGATING
SYSTEM
.
291
7
CONCLUDINGADDRESS
.292
REFERENCES
.
293
A
CHAOS
AND
FRACTAL
DYNAMIC
APPROACH
TO
THE
FRACTURE
MECHANICS
L.M.
ALVES,
R.F.M.
LOBO
.
295
1
INTRODUCTION
.
295
2
THEORETICAL
DEVELOPMENT
OF
A
CHAOTIC
MODEL
TO
DYNAMIC
FRACTURE.
297
3
RESULTS.309
4
DISCUSSION.313
5
SUMMARY
AND
CONCLUSIONS.
313
REFERENCES
.
315
NONLINEAR
DYNAMICS
AND
FRACTAL
AVALANCHES
IN
A
PILE
OF
RICE
R.J.
WIJNGAARDEN,
K.A.
LYYORINCZ,
C.M.
AEGERTER
.
317
1
INTRODUCTION
.
317
2
EXPERIMENT:ABIGRICEPILE.318
3
THEROUGHSURFACEOFTHEPILE
.320
4
AVALANCHES
ON
THE
RICE
PILE
.
322
5
RELATION
BETWEEN
AVALANCHES
AND
SURFACE
.
324
6
AVALANCHES
AS
SPATIOTEMPORAL
FRACTALS
.
326
7
HOW
TO
PREVENT
AVALANCHES.
328
8
CONCLUSIONS.333
REFERENCES
.
334
XIV
CONTENTS
PART
V
MISCELLANEOUS
A
RECENT
APPRECIATION
OF
THE
SINGULAR
DYNAMICS
AT
THE
EDGE
OF
CHAOS
E.
MAYORAL,
A.
ROBLEDO
.
339
1
INTRODUCTION
.
339
2
CRITICAL
ATTRACTORS
IN
THE
LOGISTIC
MAP.
341
3
MORI'S
Q
-PHASE
TRANSITIONS
IN
THE
LOGISTIC
MAP.
342
4
TSALLIS
DYNAMICS
AT
THE
EDGE
OF
CHAOS.
343
5
A
FAMILY
OF
Q
-PHASE
TRANSITIONS
AT
THE
EDGE
OF
CHAOS
.
346
6
NOISY
DYNAMICS
AT
THE
EDGE
OF
CHAOS.
348
7
ANALOGY
WITH
GLASSY
DYNAMICS
.
350
8
CONCLUDINGREMARKS.352
REFERENCES
.
353
QUANTUM
CHAOS
VERSUS
CLASSICAL
CHAOS:
WHY
IS
QUANTUM
CHAOS
WEAKER?
H.
KR¨OGER,
J.-F.
LAPRISE,
G.
MELKONYAN,
R.
ZOMORRODI
.
355
1
INTRODUCTION
.
355
2
CASES
WHERE
QUANTUM
CHAOS
WAS
FOUND
TOBEWEAKER.356
3
UNIFORM
DESCRIPTION
OF
CHAOS.
358
4
RENORMALISATION
FLOW
OF
PARAMETERS
OF
THE
QUANTUM
ACTION
.
362
5
INTERPRETATION.
366
REFERENCES
.
367
ON
THE
PREDICTION
OF
CHAOS
IN
THE
RESTRICTED
THREE-BODY
PROBLEM
HOUMAN
SAFAAI,
MOHAMMAD
HASAN
GHAFFARI
SAADAT
.
369
1
INTRODUCTION
.
369
2
THE
RELATIONSHIP
BETWEEN
MECHANICS
AND
RIEMANNIAN
GEOMETRY
.
370
3
NUMERICAL
COMPUTATION
FOR
RESTRICTED
THREE-BODY
PROBLEM
.
376
4
CONCLUSION
.382
REFERENCES
.
383
ORDER
AND
CHAOS
IN
SOME
HAMILTONIAN
SYSTEMS
OF
INTEREST
IN
PLASMA
PHYSICS
D.
CONSTANTINESCU,
B.
WEYSSOW
.
385
1
INTRODUCTION
.
385
2
THE
MATHEMATICAL
MODELS.
386
3
DEFINITIONS
AND
BASIC
RESULTS
.
389
4
TRANSPORTBARRIERS.394
CONTENTS
XV
5
RECONNECTION
AND
TRANSPORT
BARRIERS
.
400
6
CONCLUSIONS.402
REFERENCES
.
404
INDEX
.407 |
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| genre | (DE-588)4143413-4 Aufsatzsammlung gnd-content |
| genre_facet | Aufsatzsammlung |
| id | DE-604.BV021484445 |
| illustrated | Illustrated |
| index_date | 2024-07-02T14:08:33Z |
| indexdate | 2024-07-09T20:36:31Z |
| institution | BVB |
| isbn | 9783540283669 3540283668 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014683370 |
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| physical | XX, 411 S. Ill., graph. Darst. 24 cm |
| publishDate | 2006 |
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| publisher | Springer |
| record_format | marc |
| series2 | Springer complexity Understanding complex systems |
| spelling | The logistic map and the route to chaos from the beginnings to modern applications M. Ausloos ; M. Dirickx (ed.) Berlin ; Heidelberg ; New York Springer 2006 XX, 411 S. Ill., graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Springer complexity Understanding complex systems Literaturangaben Verhulst, P.-F <1804-1849> - (Pierre François) Verhulst, P.-F <1804-1849> (Pierre François) Chaos Chaotic behavior in systems Chaostheorie (DE-588)4009754-7 gnd rswk-swf (DE-588)4143413-4 Aufsatzsammlung gnd-content Chaostheorie (DE-588)4009754-7 s DE-604 Ausloos, Marcel Sonstige oth DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014683370&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | The logistic map and the route to chaos from the beginnings to modern applications Verhulst, P.-F <1804-1849> - (Pierre François) Verhulst, P.-F <1804-1849> (Pierre François) Chaos Chaotic behavior in systems Chaostheorie (DE-588)4009754-7 gnd |
| subject_GND | (DE-588)4009754-7 (DE-588)4143413-4 |
| title | The logistic map and the route to chaos from the beginnings to modern applications |
| title_auth | The logistic map and the route to chaos from the beginnings to modern applications |
| title_exact_search | The logistic map and the route to chaos from the beginnings to modern applications |
| title_exact_search_txtP | The logistic map and the route to chaos from the beginnings to modern applications |
| title_full | The logistic map and the route to chaos from the beginnings to modern applications M. Ausloos ; M. Dirickx (ed.) |
| title_fullStr | The logistic map and the route to chaos from the beginnings to modern applications M. Ausloos ; M. Dirickx (ed.) |
| title_full_unstemmed | The logistic map and the route to chaos from the beginnings to modern applications M. Ausloos ; M. Dirickx (ed.) |
| title_short | The logistic map and the route to chaos |
| title_sort | the logistic map and the route to chaos from the beginnings to modern applications |
| title_sub | from the beginnings to modern applications |
| topic | Verhulst, P.-F <1804-1849> - (Pierre François) Verhulst, P.-F <1804-1849> (Pierre François) Chaos Chaotic behavior in systems Chaostheorie (DE-588)4009754-7 gnd |
| topic_facet | Verhulst, P.-F <1804-1849> - (Pierre François) Verhulst, P.-F <1804-1849> (Pierre François) Chaos Chaotic behavior in systems Chaostheorie Aufsatzsammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014683370&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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