Stability of vector differential delay equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Basel [u.a.]
Springer
2013
|
| Schriftenreihe: | Frontiers in mathematics
|
| Online-Zugang: | BTU01 TUM01 UBA01 UBM01 UBT01 UBW01 UPA01 Volltext Inhaltsverzeichnis Abstract |
| Beschreibung: | 1 Online-Ressource |
| ISBN: | 9783034805766 9783034805773 |
| DOI: | 10.1007/978-3-0348-0577-3 |
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Datensatz im Suchindex
| _version_ | 1804150205747036160 |
|---|---|
| adam_text | STABILITY OF VECTOR DIFFERENTIAL DELAY EQUATIONS
/ GIL’, MICHAEL I.
: 2013
TABLE OF CONTENTS / INHALTSVERZEICHNIS
PREFACE
1 PRELIMINARIES
2 SOME RESULTS OF THE MATRIX THEORY
3 GENERAL LINEAR SYSTEMS
4 TIME-INVARIANT LINEAR SYSTEMS WITH DELAY
5 PROPERTIES OF CHARACTERISTIC VALUES
6 EQUATIONS CLOSE TO AUTONOMOUS AND ORDINARY DIFFERENTIAL ONES
7 PERIODIC SYSTEMS
8 LINEAR EQUATIONS WITH OSCILLATING COEFFICIENTS
9 LINEAR EQUATIONS WITH SLOWLY VARYING COEFFICIENTS
10 NONLINEAR VECTOR EQUATIONS
11 SCALAR NONLINEAR EQUATIONS
12 FORCED OSCILLATIONS IN VECTOR SEMI-LINEAR EQUATIONS
13 STEADY STATES OF DIFFERENTIAL DELAY EQUATIONS
14 MULTIPLICATIVE REPRESENTATIONS OF SOLUTIONS
APPENDIX A. THE GENERAL FORM OF CAUSAL OPERATORS
APPENDIX B. INFINITE BLOCK MATRICES
BIBLIOGRAPHY
INDEX.
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
STABILITY OF VECTOR DIFFERENTIAL DELAY EQUATIONS
/ GIL’, MICHAEL I.
: 2013
ABSTRACT / INHALTSTEXT
DIFFERENTIAL EQUATIONS WITH DELAY NATURALLYARISE IN VARIOUS
APPLICATIONS, SUCH AS CONTROL SYSTEMS, VISCOELASTICITY, MECHANICS,
NUCLEAR REACTORS, DISTRIBUTED NETWORKS, HEAT FLOWS, NEURAL NETWORKS,
COMBUSTION, INTERACTION OF SPECIES, MICROBIOLOGY, LEARNING MODELS,
EPIDEMIOLOGY, PHYSIOLOGY, AND MANY OTHERS. THIS BOOK SYSTEMATICALLY
INVESTIGATES THE STABILITY OF LINEAR AS WELL AS NONLINEAR VECTOR
DIFFERENTIAL EQUATIONS WITH DELAY AND EQUATIONS WITH CAUSAL MAPPINGS. IT
PRESENTS EXPLICIT CONDITIONS FOR EXPONENTIAL, ABSOLUTE AND
INPUT-TO-STATE STABILITIES. THESE STABILITY CONDITIONS ARE MAINLY
FORMULATED IN TERMS OF THE DETERMINANTS AND EIGENVALUES OF AUXILIARY
MATRICES DEPENDENT ON A PARAMETER; THE SUGGESTED APPROACHALLOWS US TO
APPLY THE WELL-KNOWN RESULTS OF THE THEORY OF MATRICES. IN ADDITION,
SOLUTION ESTIMATES FOR THE CONSIDERED EQUATIONS ARE ESTABLISHED WHICH
PROVIDE THE BOUNDS FOR REGIONS OF ATTRACTION OF STEADY STATES. THE
MAIN METHODOLOGY PRESENTED IN THE BOOK IS BASED ON A COMBINED USAGE OF
THE RECENT NORM ESTIMATES FOR MATRIX-VALUED FUNCTIONSAND THE FOLLOWING
METHODS AND RESULTS: THE GENERALIZED BOHL-PERRON PRINCIPLE AND THE
INTEGRAL VERSION OF THE GENERALIZED BOHL-PERRON PRINCIPLE; THE FREEZING
METHOD; THE POSITIVITY OF FUNDAMENTAL SOLUTIONS. A SIGNIFICANT PART OF
THE BOOK IS DEVOTED TO THE AIZERMAN-MYSHKIS PROBLEM AND GENERALIZED
HILL THEORY OF PERIODIC SYSTEMS. THE BOOK IS INTENDED NOT ONLY FOR
SPECIALISTS IN THE THEORY OF FUNCTIONAL DIFFERENTIAL EQUATIONS AND
CONTROL THEORY, BUT ALSO FOR ANYONE WITH A SOUND MATHEMATICAL BACKGROUND
INTERESTED IN THEIR VARIOUS APPLICATIONS
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-0348-0577-3 |
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| spelling | Gil', Michail I. 1941- Verfasser (DE-588)128577916 aut Stability of vector differential delay equations Michael I. Gilʹ Basel [u.a.] Springer 2013 1 Online-Ressource txt rdacontent c rdamedia cr rdacarrier Frontiers in mathematics https://doi.org/10.1007/978-3-0348-0577-3 Verlag Volltext Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025892913&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025892913&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Abstract |
| spellingShingle | Gil', Michail I. 1941- Stability of vector differential delay equations |
| title | Stability of vector differential delay equations |
| title_auth | Stability of vector differential delay equations |
| title_exact_search | Stability of vector differential delay equations |
| title_full | Stability of vector differential delay equations Michael I. Gilʹ |
| title_fullStr | Stability of vector differential delay equations Michael I. Gilʹ |
| title_full_unstemmed | Stability of vector differential delay equations Michael I. Gilʹ |
| title_short | Stability of vector differential delay equations |
| title_sort | stability of vector differential delay equations |
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