Dynamical systems: stability, controllability and chaotic behavior
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Heidelberg
Springer
2010
|
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | X, 238 S. Ill., graph. Darst. 24 cm |
| ISBN: | 9783642137211 |
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Record in the Search Index
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| adam_text |
CONTENTS 1 UNCONTROLLED SYSTEMS 1 1.1 ABSTRACT DEFINITION OF DYNAMICAL
SYSTEMS 1 1.2 TIME-CONTINUOUS DYNAMICAL SYSTEMS 4 1.2.1 ELEMENTARY
PROPERTIES 4 1.2.2 SYSTEMS IN THE PLANE 8 1.2.3 STABILITY: THE DIRECT
METHOD OF LYAPUNOV 14 1.2.4 APPLICATION TO A GENERAL PREDATOR-PREY MODEL
21 1.2.5 APPLICATION TO EVOLUTION MATRIX GAMES 32 1.3 TIME-DISCRETE
DYNAMICAL SYSTEMS 36 1.3.1 THE AUTONOMOUS CASE: DEFINITIONS AND
ELEMENTARY PROPERTIES 36 1.3.2 LOCALIZATION OF LIMIT SETS WITH THE AID
OF LYAPUNOV FUNCTIONS 40 1.3.3 STABILITY BASED ON LYAPUNOV'S METHOD 42
1.3.4 STABILITY OF FIXED POINTS VIA LINEARISATION 47 1.3.5 LINEAR
SYSTEMS 50 1.3.6 DISCRETIZATION OF TIME-CONTINUOUS DYNAMICAL SYSTEMS .
55 1.3.7 APPLICATIONS 57 1.3.8 THE NON-AUTONOMOUS CASE: DEFINITIONS AND
ELEMENTARY PROPERTIES 62 1.3.9 STABILITY BASED ON LYAPUNOV'S METHOD 64
1.3.10 LINEAR SYSTEMS 67 1.3.11 APPLICATION TO A MODEL FOR THE PROCESS
OF HEMO-DIALYSIS 73 2 CONTROLLED SYSTEMS 77 2.1 THE TIME-CONTINUOUS CASE
77 2.1.1 THE PROBLEM OF CONTROLLABILITY 77 2.1.2 CONTROLLABILITY OF
LINEAR SYSTEMS 78 2.1.3 RESTRICTED NULL-CONTROLLABILITY OF LINEAR
SYSTEMS 82 2.1.4 CONTROLLABILITY OF NONLINEAR SYSTEMS INTO REST POINTS
. 85 BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1002540968
DIGITALISIERT DURCH X CONTENTS 2.1.5 APPROXIMATE SOLUTION OF THE PROBLEM
OF RESTRICTED NULL-CONTROLLABILITY 89 2.1.6 TIME-MINIMAL RESTRICTED
NULL-CONTROLLABILITY OF LINEAR SYSTEMS 91 2.2 THE TIME-DISCRETE
AUTONOMOUS CASE 101 2.2.1 THE PROBLEM OF FIXED POINT CONTROLLABILITY 101
2.2.2 NULL-CONTROLLABILITY OF LINEAR SYSTEMS ILL 2.2.3 A METHOD FOR
SOLVING THE PROBLEM OF NULL-CONTROLLABILITYLL8 2.2.4 STABILIZATION OF
CONTROLLED SYSTEMS 124 2.2.5 APPLICATIONS 126 2.3 THE TIME-DISCRETE
NON-AUTONOMOUS CASE 134 2.3.1 THE PROBLEM OF FIXED POINT CONTROLLABILITY
134 2.3.2 THE GENERAL PROBLEM OF CONTROLLABILITY 138 2.3.3 STABILIZATION
OF CONTROLLED SYSTEMS 141 2.3.4 THE PROBLEM OF REACHABILITY 143 3
CHAOTIC BEHAVIOR OF AUTONOMOUS TIME-DISCRETE SYSTEMS . 149 3.1 CHAOS IN
THE SENSE OF DEVANEY 149 3.2 TOPOLOGICAL CONJUGACY 154 3.3 THE
TOPOLOGICAL ENTROPY AS A MEASURE FOR CHAOS 163 3.3.1 DEFINITION AND
INVARIANCE 163 3.3.2 THE TOPOLOGICAL ENTROPY OF THE SHIFT-MAPPING 165
3.3.3 DISORDER-CHAOS FOR ONE-DIMENSIONAL MAPPINGS 167 3.4 CHAOS IN THE
SENSE OF LI AND YORKE 172 3.5 STRANGE (OR CHAOTIC) ATTRACTORS 180 3.6
BIBLIOGRAPHICAL REMARKS 190 A A DYNAMICAL METHOD FOR THE CALCULATION OF
NASH- EQUILIBRIA IN N*PERSON GAMES 195 A.I THE FIXED POINT THEOREMS OF
BROUWER AND KAKUTANI 195 A.2 NASH EQUILIBRIA AS FIXED POINTS OF MAPPINGS
197 A. |
| any_adam_object | 1 |
| author | Krabs, Werner 1934-2017 Pickl, Stefan 1967- |
| author_GND | (DE-588)120318741 (DE-588)12132799X |
| author_facet | Krabs, Werner 1934-2017 Pickl, Stefan 1967- |
| author_role | aut aut |
| author_sort | Krabs, Werner 1934-2017 |
| author_variant | w k wk s p sp |
| building | Verbundindex |
| bvnumber | BV039135875 |
| classification_rvk | SK 350 SK 520 |
| ctrlnum | (OCoLC)670205011 (DE-599)DNB1002540968 |
| dewey-full | 515.39 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.39 |
| dewey-search | 515.39 |
| dewey-sort | 3515.39 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| isbn | 9783642137211 |
| language | English |
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| physical | X, 238 S. Ill., graph. Darst. 24 cm |
| publishDate | 2010 |
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| publishDateSort | 2010 |
| publisher | Springer |
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| spelling | Krabs, Werner 1934-2017 Verfasser (DE-588)120318741 aut Dynamical systems stability, controllability and chaotic behavior Werner Krabs ; Stefan Pickl Berlin ; Heidelberg Springer 2010 X, 238 S. Ill., graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Literaturangaben Dynamisches System (DE-588)4013396-5 gnd rswk-swf Stabilität (DE-588)4056693-6 gnd rswk-swf Steuerbarkeit (DE-588)4134713-4 gnd rswk-swf Chaotisches System (DE-588)4316104-2 gnd rswk-swf Dynamisches System (DE-588)4013396-5 s Steuerbarkeit (DE-588)4134713-4 s Stabilität (DE-588)4056693-6 s Chaotisches System (DE-588)4316104-2 s DE-604 Pickl, Stefan 1967- Verfasser (DE-588)12132799X aut X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3476856&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024154058&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Krabs, Werner 1934-2017 Pickl, Stefan 1967- Dynamical systems stability, controllability and chaotic behavior Dynamisches System (DE-588)4013396-5 gnd Stabilität (DE-588)4056693-6 gnd Steuerbarkeit (DE-588)4134713-4 gnd Chaotisches System (DE-588)4316104-2 gnd |
| subject_GND | (DE-588)4013396-5 (DE-588)4056693-6 (DE-588)4134713-4 (DE-588)4316104-2 |
| title | Dynamical systems stability, controllability and chaotic behavior |
| title_auth | Dynamical systems stability, controllability and chaotic behavior |
| title_exact_search | Dynamical systems stability, controllability and chaotic behavior |
| title_full | Dynamical systems stability, controllability and chaotic behavior Werner Krabs ; Stefan Pickl |
| title_fullStr | Dynamical systems stability, controllability and chaotic behavior Werner Krabs ; Stefan Pickl |
| title_full_unstemmed | Dynamical systems stability, controllability and chaotic behavior Werner Krabs ; Stefan Pickl |
| title_short | Dynamical systems |
| title_sort | dynamical systems stability controllability and chaotic behavior |
| title_sub | stability, controllability and chaotic behavior |
| topic | Dynamisches System (DE-588)4013396-5 gnd Stabilität (DE-588)4056693-6 gnd Steuerbarkeit (DE-588)4134713-4 gnd Chaotisches System (DE-588)4316104-2 gnd |
| topic_facet | Dynamisches System Stabilität Steuerbarkeit Chaotisches System |
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