Numerical continuation of periodic orbits with symmetry:
Abstract: "We consider periodic orbits of autonomous parameter dependent ODE's. Starting from a shooting algorithm for the numerical computation of periodic orbits via an adaptive Poincaré-section we develop a pathfollowing algorithm for periodic solutions based on a tangential continuatio...
Gespeichert in:
| Hauptverfasser: | , , |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin
Konrad-Zuse-Zentrum für Informationstechnik
1994
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| Schriftenreihe: | Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC
1994,12 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | Abstract: "We consider periodic orbits of autonomous parameter dependent ODE's. Starting from a shooting algorithm for the numerical computation of periodic orbits via an adaptive Poincaré-section we develop a pathfollowing algorithm for periodic solutions based on a tangential continuation method with implicit reparametrization. For ODE's equivariant w.r.t. a finite group we show that spatial as well as spatio-temporal symmetries of periodic orbits can be exploited within the (multiple) shooting context. We describe how turning points, period doubling bifurcations and Hopf points along the branch of periodic solutions can be handled. Furthermore equivariant Hopf points and generic secondary bifurcations of periodic orbits with Z[subscript m]-symmetry are treated. We tested the code with standard examples, e.g., the period doubling cascade in the Lorenz equations. To show the efficiency of the described methods we also used the program for an application from electronics, a ring oscillator with n inverters. In this example the exploitation of symmetry reduces the amount of work for the continuation of periodic orbits from O(n²) to O(n)." |
| Beschreibung: | 27 S. graph. Darst. |
Internformat
MARC
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| 100 | 1 | |a Wulff, Claudia |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Numerical continuation of periodic orbits with symmetry |c Claudia Wulff ; Andreas Hohmann ; Peter Deuflhard |
| 264 | 1 | |a Berlin |b Konrad-Zuse-Zentrum für Informationstechnik |c 1994 | |
| 300 | |a 27 S. |b graph. Darst. | ||
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| 490 | 1 | |a Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC |v 1994,12 | |
| 520 | 3 | |a Abstract: "We consider periodic orbits of autonomous parameter dependent ODE's. Starting from a shooting algorithm for the numerical computation of periodic orbits via an adaptive Poincaré-section we develop a pathfollowing algorithm for periodic solutions based on a tangential continuation method with implicit reparametrization. For ODE's equivariant w.r.t. a finite group we show that spatial as well as spatio-temporal symmetries of periodic orbits can be exploited within the (multiple) shooting context. We describe how turning points, period doubling bifurcations and Hopf points along the branch of periodic solutions can be handled. Furthermore equivariant Hopf points and generic secondary bifurcations of periodic orbits with Z[subscript m]-symmetry are treated. We tested the code with standard examples, e.g., the period doubling cascade in the Lorenz equations. To show the efficiency of the described methods we also used the program for an application from electronics, a ring oscillator with n inverters. In this example the exploitation of symmetry reduces the amount of work for the continuation of periodic orbits from O(n²) to O(n)." | |
| 650 | 4 | |a Differential equations | |
| 700 | 1 | |a Hohmann, Andreas |d 1953- |e Verfasser |0 (DE-588)110521102 |4 aut | |
| 700 | 1 | |a Deuflhard, Peter |d 1944-2019 |e Verfasser |0 (DE-588)108205983 |4 aut | |
| 830 | 0 | |a Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC |v 1994,12 |w (DE-604)BV004801715 |9 1994,12 | |
| 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=006450761&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-006450761 | |
Datensatz im Suchindex
| _version_ | 1816443231479529472 |
|---|---|
| adam_text |
CONTENTS
INTRODUCTION
1
1
COMPUTATION
OF
SINGLE
PERIODIC
ORBITS
2
2
CONTINUATION
OF
PERIODIC
ORBITS
5
3
EXPLOITATION
OF
SYMMETRY
9
4
COMPUTATION
OF
BIFURCATIONS
11
4.1
GENERIC
BIFURCATIONS
WITHOUT
SYMMETRY
.
11
4.2
SYMMETRY-BREAKING
BIFURCATIONS
.
15
5
EXAMPLES
18
REFERENCES
26 |
| any_adam_object | 1 |
| author | Wulff, Claudia Hohmann, Andreas 1953- Deuflhard, Peter 1944-2019 |
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| author_sort | Wulff, Claudia |
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| bvnumber | BV009753394 |
| ctrlnum | (OCoLC)32498974 (DE-599)BVBBV009753394 |
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| id | DE-604.BV009753394 |
| illustrated | Illustrated |
| indexdate | 2024-11-22T17:07:34Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006450761 |
| oclc_num | 32498974 |
| open_access_boolean | |
| owner | DE-12 |
| owner_facet | DE-12 |
| physical | 27 S. graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Konrad-Zuse-Zentrum für Informationstechnik |
| record_format | marc |
| series | Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC |
| series2 | Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC |
| spelling | Wulff, Claudia Verfasser aut Numerical continuation of periodic orbits with symmetry Claudia Wulff ; Andreas Hohmann ; Peter Deuflhard Berlin Konrad-Zuse-Zentrum für Informationstechnik 1994 27 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC 1994,12 Abstract: "We consider periodic orbits of autonomous parameter dependent ODE's. Starting from a shooting algorithm for the numerical computation of periodic orbits via an adaptive Poincaré-section we develop a pathfollowing algorithm for periodic solutions based on a tangential continuation method with implicit reparametrization. For ODE's equivariant w.r.t. a finite group we show that spatial as well as spatio-temporal symmetries of periodic orbits can be exploited within the (multiple) shooting context. We describe how turning points, period doubling bifurcations and Hopf points along the branch of periodic solutions can be handled. Furthermore equivariant Hopf points and generic secondary bifurcations of periodic orbits with Z[subscript m]-symmetry are treated. We tested the code with standard examples, e.g., the period doubling cascade in the Lorenz equations. To show the efficiency of the described methods we also used the program for an application from electronics, a ring oscillator with n inverters. In this example the exploitation of symmetry reduces the amount of work for the continuation of periodic orbits from O(n²) to O(n)." Differential equations Hohmann, Andreas 1953- Verfasser (DE-588)110521102 aut Deuflhard, Peter 1944-2019 Verfasser (DE-588)108205983 aut Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC 1994,12 (DE-604)BV004801715 1994,12 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006450761&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wulff, Claudia Hohmann, Andreas 1953- Deuflhard, Peter 1944-2019 Numerical continuation of periodic orbits with symmetry Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC Differential equations |
| title | Numerical continuation of periodic orbits with symmetry |
| title_auth | Numerical continuation of periodic orbits with symmetry |
| title_exact_search | Numerical continuation of periodic orbits with symmetry |
| title_full | Numerical continuation of periodic orbits with symmetry Claudia Wulff ; Andreas Hohmann ; Peter Deuflhard |
| title_fullStr | Numerical continuation of periodic orbits with symmetry Claudia Wulff ; Andreas Hohmann ; Peter Deuflhard |
| title_full_unstemmed | Numerical continuation of periodic orbits with symmetry Claudia Wulff ; Andreas Hohmann ; Peter Deuflhard |
| title_short | Numerical continuation of periodic orbits with symmetry |
| title_sort | numerical continuation of periodic orbits with symmetry |
| topic | Differential equations |
| topic_facet | Differential equations |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006450761&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004801715 |
| work_keys_str_mv | AT wulffclaudia numericalcontinuationofperiodicorbitswithsymmetry AT hohmannandreas numericalcontinuationofperiodicorbitswithsymmetry AT deuflhardpeter numericalcontinuationofperiodicorbitswithsymmetry |