Stability and oscillations in delay differential equations of population dynamics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht u.a.
Kluwer Acad.
1992
|
| Schriftenreihe: | Mathematics and its applications
74 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 501 S. |
| ISBN: | 0792315944 |
Internformat
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| 100 | 1 | |a Gopalsamy, K. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Stability and oscillations in delay differential equations of population dynamics |c by K. Gopalsamy |
| 264 | 1 | |a Dordrecht u.a. |b Kluwer Acad. |c 1992 | |
| 300 | |a XII, 501 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematics and its applications |v 74 | |
| 650 | 4 | |a Oscillations | |
| 650 | 4 | |a Population | |
| 650 | 4 | |a Stabilité | |
| 650 | 4 | |a Équations différentielles à retard | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Delay differential equations | |
| 650 | 4 | |a Oscillations | |
| 650 | 4 | |a Population |x Mathematical models | |
| 650 | 4 | |a Stability | |
| 650 | 0 | 7 | |a Differentialgleichung mit nacheilendem Argument |0 (DE-588)4199298-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Schwingung |0 (DE-588)4053999-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Stabilität |0 (DE-588)4056693-6 |2 gnd |9 rswk-swf |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-003222811 | ||
Datensatz im Suchindex
| _version_ | 1804119368336932864 |
|---|---|
| adam_text | CONTENTS
SERIES EDITOR S PREFACE v
PREFACE ix
CHAPTER 1. THE DELAY LOGISTIC EQUATION
1.1. Introduction 1
1.2. Linear stability criteria 3
1.3. Linear oscillators and comparison 37
1.4. Global stability 55
1.5. Oscillation and nonoscillation 66
1.6. Piecewise constant arguments and impulses 78
1.7. Feedback control 95
Exercises I 102
CHAPTER 2. DELAY INDUCED BIFURCATION TO PERIODICITY
2.1. Introduction 124
2.2. Loss of linear stability 128
2.3. Delay induced bifurcation to periodicity 130
2.4. Stability of the bifurcating periodic solution 136
2.5. An example 143
2.6. Coupled oscillators 148
Exercises II 160
CHAPTER 3. METHODS OF LINEAR ANALYSIS
3.1. Preliminary remarks 172
3.2. Delays in production 175
3.3. Competition and cooperation 182
3.4. Prey predator systems 196
3.5. Delays in production and destruction 204
3.6. X(t) = AX(t) + BX(t t) 210
3.7. Stability switches 239
3.8. Oscillations in linear systems 253
3.9. Simple stability criteria 263
Exercises III 273
viii
CHAPTER 4. GLOBAL ATTRACTIVITY
4.1. Some preliminaries 292
4.2. Competition : exploitation and interference 298
4.3. Delays in competition and cooperation 306
4.4. Method of Lyapunov functionals 327
4.5. Oscillations in Lotka Volterra systems 340
4.6. Why positive steady states ? 346
4.7. Dynamics in compartments 355
Exercises IV 370
CHAPTER 5. MODELS OF NEUTRAL DIFFERENTIAL SYSTEMS
5.1. Linear scalar equations 393
5.2. Oscillation criteria 399
5.3. Neutral logistic equation 418
5.4. A Neutral Lotka Volterra system 430
5.5. X(t) = AX(t) + BX(t t) + CX(t r) 436
5.6. Large scale systems 447
Exercises V 462
REFERENCES 474
INDEX 497
|
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| id | DE-604.BV005203958 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:25:05Z |
| institution | BVB |
| isbn | 0792315944 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003222811 |
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| physical | XII, 501 S. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | Kluwer Acad. |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Gopalsamy, K. Verfasser aut Stability and oscillations in delay differential equations of population dynamics by K. Gopalsamy Dordrecht u.a. Kluwer Acad. 1992 XII, 501 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 74 Oscillations Population Stabilité Équations différentielles à retard Mathematisches Modell Delay differential equations Population Mathematical models Stability Differentialgleichung mit nacheilendem Argument (DE-588)4199298-2 gnd rswk-swf Schwingung (DE-588)4053999-4 gnd rswk-swf Stabilität (DE-588)4056693-6 gnd rswk-swf Differentialgleichung mit nacheilendem Argument (DE-588)4199298-2 s Stabilität (DE-588)4056693-6 s DE-604 Schwingung (DE-588)4053999-4 s Mathematics and its applications 74 (DE-604)BV008163334 74 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003222811&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gopalsamy, K. Stability and oscillations in delay differential equations of population dynamics Mathematics and its applications Oscillations Population Stabilité Équations différentielles à retard Mathematisches Modell Delay differential equations Population Mathematical models Stability Differentialgleichung mit nacheilendem Argument (DE-588)4199298-2 gnd Schwingung (DE-588)4053999-4 gnd Stabilität (DE-588)4056693-6 gnd |
| subject_GND | (DE-588)4199298-2 (DE-588)4053999-4 (DE-588)4056693-6 |
| title | Stability and oscillations in delay differential equations of population dynamics |
| title_auth | Stability and oscillations in delay differential equations of population dynamics |
| title_exact_search | Stability and oscillations in delay differential equations of population dynamics |
| title_full | Stability and oscillations in delay differential equations of population dynamics by K. Gopalsamy |
| title_fullStr | Stability and oscillations in delay differential equations of population dynamics by K. Gopalsamy |
| title_full_unstemmed | Stability and oscillations in delay differential equations of population dynamics by K. Gopalsamy |
| title_short | Stability and oscillations in delay differential equations of population dynamics |
| title_sort | stability and oscillations in delay differential equations of population dynamics |
| topic | Oscillations Population Stabilité Équations différentielles à retard Mathematisches Modell Delay differential equations Population Mathematical models Stability Differentialgleichung mit nacheilendem Argument (DE-588)4199298-2 gnd Schwingung (DE-588)4053999-4 gnd Stabilität (DE-588)4056693-6 gnd |
| topic_facet | Oscillations Population Stabilité Équations différentielles à retard Mathematisches Modell Delay differential equations Population Mathematical models Stability Differentialgleichung mit nacheilendem Argument Schwingung Stabilität |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003222811&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008163334 |
| work_keys_str_mv | AT gopalsamyk stabilityandoscillationsindelaydifferentialequationsofpopulationdynamics |