Delay differential equations: with applications in population dynamics
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston u.a.
Acad. Press
1993
|
| Series: | Mathematics in science and engineering
191 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 398 S. grpah. Darst. |
| ISBN: | 0124276105 |
Staff View
MARC
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| 100 | 1 | |a Kuang, Yang |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Delay differential equations |b with applications in population dynamics |c Yang Kuang |
| 264 | 1 | |a Boston u.a. |b Acad. Press |c 1993 | |
| 300 | |a XII, 398 S. |b grpah. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Mathematics in science and engineering |v 191 | |
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| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Delay differential equations | |
| 650 | 4 | |a Population |x Mathematical models | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface ix
Part One: DELAY DIFFERENTIAL EQUATIONS 1
Chapter 1. Introduction 3
1.1. Delay Differential Equations from Applications 3
1.2. Small Delays Can Have Large Effects 11
1.3. Concluding Remarks 12
Chapter 2. Basic Theory of Delay Differential Equations . . 15
2.1. Preliminaries—Definitions and Notations 15
2.2. Existence, Uniqueness, Continuous Dependence, and
Smoothing Property 18
2.3. Dynamical Systems and Invariance 21
2.4. Local Stability Theory 24
2.5. The Method of Liapunov Functionals 26
2.6. Razumikhin Type Theorems 38
2.7. Infinite Delay and Fading Memory Space 46
2.8. General Linear Systems 51
2.9. Hopf Bifurcation and a Periodicity Theorem 58
Chapter 3. Characteristic Equations 63
3.1. Discrete Delays—Preliminaries 63
3.2. Discrete Delays—First Order equations 67
3.3. Discrete Delays—Second Order Equations 74
3.4. Discrete Delays—General Theory 82
v
vi Contents
3.5. Distributed Delays—Special Cases 90
3.6. Reducible Systems—The Linear Chain Trick 96
3.7. Distributed Delays—First Order Equations 98
3.8. Distributed Delays—Higher Order Equations and Systems . . 106
3.9. Remarks and Open Problems 113
Part Two: APPLICATIONS IN POPULATION DYNAMICS . . 117
Chapter 4. Global Stability for Single Species Models . . 119
4.1. Introduction 119
4.2. Wright s Global Stability Result for
y(t) = ry(t i)[i + y(t)] us
4.3. Global Stability for General Delayed Nonautonomous
Logistic Equations 126
4.4. Asymptotic Theory for Nonautonomous Delay Equations
with Negative Feedbacks 133
4.5. 3/2 Stability Results 140
4.6. A Model Exhibiting the Allee Effect 143
4.7. Equations of Type x(t) = f(xt) g(x(t))—Preliminaries . . 146
4.8. Equations of Type x(t) = f(xt) g(x(t))—When f(x)
Is Decreasing 150
4.9. Equations of Type x(t) = f(xt) g(x(t))— When f(x)
Is Increasing or Has a Hump 158
4.10. Remarks and Open Problems 170
Chapter 5. Periodic Solutions, Chaos, Structured
Single Species Models 173
5.1. Global Existence of Periodic Solutions in x(t) = f(x(t — 1))
g(*(t)) 173
5.2. Periodic Solutions in Delayed Periodic Lotka Volterra Type
Equations 181
5.3. A Model of Single Species Growth with Stage Structure . . . 187
5.4. Reduction of Structured Population Models to Threshold
Delay Equations and FDEs 191
5.5. Chaos 195
5.6. Remarks 203
Contents vii
Chapter 6. Global Stability for Multi Species Models . . 205
6.1. Introduction 205
6.2. Stability via Liapunov Functionals, I 206
6.3. Stability via Liapunov Functionals, II 211
6.4. Stability via Razumikhin Type Theorems—Theory 215
6.5. Stability via Razumikhin Type Theorems—Applications . . . 226
6.6. When Nondelayed Diagonal Terms Do Not Exist 234
6.7. Remarks and Open Problems 245
Chapter 7. Periodic Solutions in Multi Species Models . . 247
7.1. Introduction 247
7.2. Periodic Solutions in Delayed Gause Type Predator Prey
Systems 247
7.3. Periodic Solutions in Periodic Systems 263
7.4. Remarks and Open Problems 269
Chapter 8. Permanence 273
8.1. Introduction 273
8.2. Persistence in Infinite Dimensional Systems 274
8.3. Permanence in Autonomous Lotka Volterra Type Systems . . 280
8.4. Permanence in Nonautonomous Systems 285
8.5. Permanence in Nonautonomous Lotka Volterra Type
Competition Systems 297
8.6. Permanence in Nonautonomous Lotka Volterra Type
Predator Prey Systems 302
8.7. Remarks and Open Problems 309
Chapter 9. Neutral Delay Models 311
9.1. Models and Preliminaries 311
9.2. Boundedness of x(t) in the System (1.6) 315
9.3. Boundedness Results for the System (1.6) 317
9.4. Convergence in Single Population Models, I 321
9.5. Convergence in the System (1.6) 327
9.6. Convergence in Lotka—Volterra Systems 333
9.7. Convergence in Single Population Models, II 335
9.8. Boundedness in a Nonautonomous Neutral
Logistic Equation 338
viii Contents
9.9. A Periodic Neutral Logistic Equation 346
9.10. Remarks and Open Problems 350
References 353
Appendix 375
Index 395
|
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| discipline | Biologie Mathematik |
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| id | DE-604.BV007226955 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:58:00Z |
| institution | BVB |
| isbn | 0124276105 |
| language | English |
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| physical | XII, 398 S. grpah. Darst. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Acad. Press |
| record_format | marc |
| series | Mathematics in science and engineering |
| series2 | Mathematics in science and engineering |
| spelling | Kuang, Yang Verfasser aut Delay differential equations with applications in population dynamics Yang Kuang Boston u.a. Acad. Press 1993 XII, 398 S. grpah. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematics in science and engineering 191 Differentiaalvergelijkingen gtt dynamique population inriac Équations différentielles à retard ram équation différentielle avec retard inriac Mathematisches Modell Delay differential equations Population Mathematical models Populationsdynamik (DE-588)4046803-3 gnd rswk-swf Differentialgleichung mit nacheilendem Argument (DE-588)4199298-2 gnd rswk-swf Differentialgleichung mit nacheilendem Argument (DE-588)4199298-2 s Populationsdynamik (DE-588)4046803-3 s DE-604 Mathematics in science and engineering 191 (DE-604)BV000001196 191 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004628744&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kuang, Yang Delay differential equations with applications in population dynamics Mathematics in science and engineering Differentiaalvergelijkingen gtt dynamique population inriac Équations différentielles à retard ram équation différentielle avec retard inriac Mathematisches Modell Delay differential equations Population Mathematical models Populationsdynamik (DE-588)4046803-3 gnd Differentialgleichung mit nacheilendem Argument (DE-588)4199298-2 gnd |
| subject_GND | (DE-588)4046803-3 (DE-588)4199298-2 |
| title | Delay differential equations with applications in population dynamics |
| title_auth | Delay differential equations with applications in population dynamics |
| title_exact_search | Delay differential equations with applications in population dynamics |
| title_full | Delay differential equations with applications in population dynamics Yang Kuang |
| title_fullStr | Delay differential equations with applications in population dynamics Yang Kuang |
| title_full_unstemmed | Delay differential equations with applications in population dynamics Yang Kuang |
| title_short | Delay differential equations |
| title_sort | delay differential equations with applications in population dynamics |
| title_sub | with applications in population dynamics |
| topic | Differentiaalvergelijkingen gtt dynamique population inriac Équations différentielles à retard ram équation différentielle avec retard inriac Mathematisches Modell Delay differential equations Population Mathematical models Populationsdynamik (DE-588)4046803-3 gnd Differentialgleichung mit nacheilendem Argument (DE-588)4199298-2 gnd |
| topic_facet | Differentiaalvergelijkingen dynamique population Équations différentielles à retard équation différentielle avec retard Mathematisches Modell Delay differential equations Population Mathematical models Populationsdynamik Differentialgleichung mit nacheilendem Argument |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004628744&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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| work_keys_str_mv | AT kuangyang delaydifferentialequationswithapplicationsinpopulationdynamics |