Toward an understanding of stochastic Hopf bifurcation: a case study
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Bremen
Inst. für Dynamische Systeme, Fachbereich Math. und Informatik, Univ. Bremen
1996
|
| Schriftenreihe: | Institut für Dynamische Systeme <Bremen>: Report
358 |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 46 S. graph. Darst. |
Internformat
MARC
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| 041 | 0 | |a eng | |
| 049 | |a DE-12 | ||
| 100 | 1 | |a Arnold, Ludwig |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Toward an understanding of stochastic Hopf bifurcation |b a case study |c L. Arnold ; N. Sri Namachchivaya ; K. R. Schenk-Hoppé |
| 264 | 1 | |a Bremen |b Inst. für Dynamische Systeme, Fachbereich Math. und Informatik, Univ. Bremen |c 1996 | |
| 300 | |a 46 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Institut für Dynamische Systeme <Bremen>: Report |v 358 | |
| 700 | 1 | |a Namachchivaya, Navaratnam Sri |e Verfasser |4 aut | |
| 700 | 1 | |a Schenk-Hoppé, Klaus R. |e Verfasser |4 aut | |
| 830 | 0 | |a Institut für Dynamische Systeme <Bremen>: Report |v 358 |w (DE-604)BV000736900 |9 358 | |
| 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=007196964&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-007196964 | |
Datensatz im Suchindex
| _version_ | 1808137315454812160 |
|---|---|
| adam_text |
CONTENTS
1
INTRODUCTION
3
2
THE
NOISY
DUFFING-VAN
DER
POL
OSCILLATOR
4
3
RANDOM
DYNAMICAL
SYSTEMS,
LYAPUNOV
EXPONENTS
5
3.1
DEFINITION
OF
A
RANDOM
DYNAMICAL
SYSTEM
.
5
3.2
INVARIANT
MEASURES
.
6
3.3
GENERATION
OF
RANDOM
DYNAMICAL
SYSTEMS
FOR
CONTINUOUS
TIME
T
=
R
.
7
3.3.1
CASE
1:
RANDOM
DIFFERENTIAL
EQUATIONS
.
7
3.3.2
CASE
2:
STOCHASTIC
DIFFERENTIAL
EQUATIONS
.
8
3.4
LOCAL
RANDOM
DYNAMICAL
SYSTEMS
.
8
3.5
THE
MULTIPLICATIVE
ERGODIC
THEOREM
.
9
3.6
MULTIPLICATIVE
ERGODIC
THEOREM:
PARTICULAR
CASE
N
=
10
3.7
MOMENT
LYAPUNOV
EXPONENTS
.
11
3.8
INVARIANT
MANIFOLDS
.
11
3.9
APPLICATIONS
TO
THE
DUFFING-VAN
DER
POL
OSCILLATOR
.
11
4
CONCEPTS
OF
STOCHASTIC
BIFURCATION
THEORY
12
4.1
THE
PHENOMENOLOGICAL
APPROACH
.
13
4.2
THE
DYNAMICAL
APPROACH
.
14
5
FIRST
STEPS
15
5.1
ONE-DIMENSIONAL
EXAMPLE
.
15
5.2
WHAT
IS
STOCHASTIC
HOPF
BIFURCATION
?
.
17
6
APPROXIMATE
RESULTS
18
6.1
RESULTS
USING
THE
METHOD
OF
STOCHASTIC
AVERAGING
.
20
6.1.1
NONLINEAR
STATIONARY
RESPONSE
.
20
6.1.2
STABILITY
OF
STATIONARY
SOLUTIONS
.
22
6.1.3
EXPLICIT
CALCULATION
OF
THE
SOLUTION
OF
THE
AVERAGED
EQUATION
.
26
6.2
RESULTS
USING
ASYMPTOTICS
.
29
6.3
DISCUSSION
OF
RESULTS
VIA
AVERAGING
AND
ASYMPTOTICS
.
31
7
THE
METHOD
OF
STOCHASTIC
NORMAL
FORMS
32
8
NUMERICAL
SIMULATION
OF
NORMAL
FORM
35 |
| any_adam_object | 1 |
| author | Arnold, Ludwig Namachchivaya, Navaratnam Sri Schenk-Hoppé, Klaus R. |
| author_facet | Arnold, Ludwig Namachchivaya, Navaratnam Sri Schenk-Hoppé, Klaus R. |
| author_role | aut aut aut |
| author_sort | Arnold, Ludwig |
| author_variant | l a la n s n ns nsn k r s h krs krsh |
| building | Verbundindex |
| bvnumber | BV010776159 |
| ctrlnum | (OCoLC)75726098 (DE-599)BVBBV010776159 |
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| id | DE-604.BV010776159 |
| illustrated | Illustrated |
| indexdate | 2024-08-23T00:48:36Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007196964 |
| oclc_num | 75726098 |
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| owner | DE-12 |
| owner_facet | DE-12 |
| physical | 46 S. graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Inst. für Dynamische Systeme, Fachbereich Math. und Informatik, Univ. Bremen |
| record_format | marc |
| series | Institut für Dynamische Systeme <Bremen>: Report |
| series2 | Institut für Dynamische Systeme <Bremen>: Report |
| spelling | Arnold, Ludwig Verfasser aut Toward an understanding of stochastic Hopf bifurcation a case study L. Arnold ; N. Sri Namachchivaya ; K. R. Schenk-Hoppé Bremen Inst. für Dynamische Systeme, Fachbereich Math. und Informatik, Univ. Bremen 1996 46 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Institut für Dynamische Systeme <Bremen>: Report 358 Namachchivaya, Navaratnam Sri Verfasser aut Schenk-Hoppé, Klaus R. Verfasser aut Institut für Dynamische Systeme <Bremen>: Report 358 (DE-604)BV000736900 358 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007196964&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Arnold, Ludwig Namachchivaya, Navaratnam Sri Schenk-Hoppé, Klaus R. Toward an understanding of stochastic Hopf bifurcation a case study Institut für Dynamische Systeme <Bremen>: Report |
| title | Toward an understanding of stochastic Hopf bifurcation a case study |
| title_auth | Toward an understanding of stochastic Hopf bifurcation a case study |
| title_exact_search | Toward an understanding of stochastic Hopf bifurcation a case study |
| title_full | Toward an understanding of stochastic Hopf bifurcation a case study L. Arnold ; N. Sri Namachchivaya ; K. R. Schenk-Hoppé |
| title_fullStr | Toward an understanding of stochastic Hopf bifurcation a case study L. Arnold ; N. Sri Namachchivaya ; K. R. Schenk-Hoppé |
| title_full_unstemmed | Toward an understanding of stochastic Hopf bifurcation a case study L. Arnold ; N. Sri Namachchivaya ; K. R. Schenk-Hoppé |
| title_short | Toward an understanding of stochastic Hopf bifurcation |
| title_sort | toward an understanding of stochastic hopf bifurcation a case study |
| title_sub | a case study |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007196964&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000736900 |
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