Lotka-Volterra and related systems: recent developments in population dynamics
Gespeichert in:
| Weitere Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
de Gruyter
2013
|
| Schriftenreihe: | De Gruyter Series in Mathematics and Life Sciences
2 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | VIII, 236 S. Ill., graph. Darst. |
| ISBN: | 9783110269512 |
Internformat
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| 264 | 1 | |a Berlin [u.a.] |b de Gruyter |c 2013 | |
| 300 | |a VIII, 236 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a De Gruyter Series in Mathematics and Life Sciences |v 2 | |
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Lotka-Volterra equations | |
| 650 | 4 | |a Population biology |x Mathematical models | |
| 700 | 1 | |a Ahmad, Shair |4 edt | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-3-11-026984-0 |
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Datensatz im Suchindex
| _version_ | 1804151583812878336 |
|---|---|
| adam_text | CONTENTS
PREFACE V
ZHANYUAN HOU
PERMANENCE, GLOBAL ATTRACTION AND STABILITY 1
1 INTRODUCTION 1
2 EXISTENCE OF A COMPACT
UNIFORM ATTRACTOR 3
3 PROOF OF THEOREMS 2.1, 2.2 AND 2.3 8
4 PARTIAL PERMANENCE AND PERMANENCE 15
5 NECESSARY CONDITIONS FOR
PERMANENCE OF LOTKA-VOLTERRA SYSTEMS 26
6 SUFFICIENT CONDITION FOR
PERMANENCE OF LOTKA-VOLTERRA SYSTEMS 31
7 FURTHER NOTES 39
8 GLOBAL ATTRACTION AND STABILITY OF LOTKA-VOLTERRA SYSTEMS 39
9 GLOBAL STABILITY BY LYAPUNOV FUNCTIONS 40
10 GLOBAL STABILITY
BY SPLIT LYAPUNOV FUNCTIONS 42
10.1 CHECKING THE CONDITIONS (10.2) AND (10.8) 46
10.2 EXAMPLES 47
11 GLOBAL STABILITY OF COMPETITIVE LOTKA-VOLTERRA SYSTEMS 48
12 GLOBAL ATTRACTION OF COMPETITIVE LOTKA-VOLTERRA SYSTEMS 55
13 SOME NOTES*
60
BIBLIOGRAPHY 60
BENEDETTA LISENA
COMPETITIVE LOTKA-VOLTERRA SYSTEMS WITH PERIODIC COEFFICIENTS * 63
1 INTRODUCTION 63
2 THE AUTONOMOUS MODEL. THE LOGISTIC EQUATION 64
3 TWO SPECIES PERIODIC MODELS 68
4 COMPETITIVE EXCLUSION 76
5 ONE SPECIES EXTINCTION IN THREE-DIMENSIONAL MODELS 82
6 THE IMPULSIVE LOGISTIC EQUATION 91
7 TWO SPECIES SYSTEMS WITH IMPULSIVE EFFECTS. A LOOK AT THE
N-DIMENSIONAL
CASE 95
8 THE INFLUENCE OF IMPULSIVE PERTURBATIONS ON EXTINCTION IN
THREE-SPECIES
MODELS 109
BIBLIOGRAPHY 121
HTTP://D-NB.INFO/1030085900
VIII
CONTENTS
MARINA PIREDDU AND FABIO ZANOLIN
FIXED POINTS, PERIODIC POINTS AND CHAOTIC DYNAMICS FOR CONTINUOUS MAPS
WITH
APPLICATIONS TO POPULATION DYNAMICS 123
1 INTRODUCTION 123
2 NOTATION 125
3 SEARCH OF FIXED POINTS FOR MAPS EXPANSIVE ALONG ONE DIRECTION 127
4 THE PLANAR CASE 128
4.1 STRETCHING ALONG
THE PATHS AND VARIANTS 128
4.2 THE CROSSING LEMMA 143
5 THE N-DIMENSIONAL SETTING: INTERSECTION LEMMA 152
5.1 ZERO-SETS OF MAPS DEPENDING ON PARAMETERS 157
5.2 STRETCHING ALONG
THE PATHS IN THE
IV-DIMENSIONAL CASE 163
6 CHAOTIC DYNAMICS FOR CONTINUOUS MAPS 168
7 DEFINITIONS AND MAIN RESULTS 172
8 SYMBOLIC DYNAMICS 181
9 ON VARIOUS NOTIONS OF CHAOS 190
10 LINKED TWIST MAPS*198
11 EXAMPLES FROM THE ODES 206
12 PREDATOR-PREY MODEL 207
12.1 THE EFFECTS OF A PERIODIC HARVESTING 207
12.2
TECHNICAL DETAILS AND PROOFS 215
BIBLIOGRAPHY 225
INDEX 235
|
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| indexdate | 2024-07-10T00:57:08Z |
| institution | BVB |
| isbn | 9783110269512 |
| language | English |
| lccn | 012051182 |
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| physical | VIII, 236 S. Ill., graph. Darst. |
| publishDate | 2013 |
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| series | De Gruyter Series in Mathematics and Life Sciences |
| series2 | De Gruyter Series in Mathematics and Life Sciences |
| spelling | Lotka-Volterra and related systems recent developments in population dynamics edited by Shair Ahmad ... Berlin [u.a.] de Gruyter 2013 VIII, 236 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier De Gruyter Series in Mathematics and Life Sciences 2 Includes bibliographical references and index Mathematisches Modell Lotka-Volterra equations Population biology Mathematical models Ahmad, Shair edt Erscheint auch als Online-Ausgabe 978-3-11-026984-0 De Gruyter Series in Mathematics and Life Sciences 2 (DE-604)BV040694965 2 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026902962&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lotka-Volterra and related systems recent developments in population dynamics De Gruyter Series in Mathematics and Life Sciences Mathematisches Modell Lotka-Volterra equations Population biology Mathematical models |
| title | Lotka-Volterra and related systems recent developments in population dynamics |
| title_auth | Lotka-Volterra and related systems recent developments in population dynamics |
| title_exact_search | Lotka-Volterra and related systems recent developments in population dynamics |
| title_full | Lotka-Volterra and related systems recent developments in population dynamics edited by Shair Ahmad ... |
| title_fullStr | Lotka-Volterra and related systems recent developments in population dynamics edited by Shair Ahmad ... |
| title_full_unstemmed | Lotka-Volterra and related systems recent developments in population dynamics edited by Shair Ahmad ... |
| title_short | Lotka-Volterra and related systems |
| title_sort | lotka volterra and related systems recent developments in population dynamics |
| title_sub | recent developments in population dynamics |
| topic | Mathematisches Modell Lotka-Volterra equations Population biology Mathematical models |
| topic_facet | Mathematisches Modell Lotka-Volterra equations Population biology Mathematical models |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026902962&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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