Exactly solvable models of biological invasion:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton [u.a.]
Chapman & Hall/CRC
2005
|
| Schriftenreihe: | Chapman & Hall/CRC mathematical biology and medicine series
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | 217 S. graph. Darst., Kt. 25cm |
| ISBN: | 9781584885214 1584885211 |
Internformat
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| 100 | 1 | |a Petrovskii, Sergei V. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Exactly solvable models of biological invasion |c Sergei V. Petrovskii and Bai-Lian Li |
| 264 | 1 | |a Boca Raton [u.a.] |b Chapman & Hall/CRC |c 2005 | |
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| 500 | |a Includes bibliographical references and index | ||
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Datensatz im Suchindex
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|---|---|
| adam_text | Chapman amp; Hall/CRC Mathematical Biology and Medicine Series
EXACTLY SOLVABLE MODELS
OF BIOLOGICAL INVASION
SERGEI V PETROVSKII AND BAI-LIAN LI
Chapman amp; Hall/CRC
Taylor amp; Francis Croup
Boca Raton London New York Singapore
Contents
Introduction 1
1 1 Why exactly solvable models are important 1
1 2 Intra- and inter-species interactions and local population dy-
namics 5
1 3 Basic mechanisms of species transport 11
1 4 Biological invasion: main facts and constituting examples 14
Models of biological invasion 17
2 1 Diffusion-reaction equations 17
2 2 Integral-difference models 24
2 3 Space-discrete models 30
2 4 Stochastic models 39
2 5 Concluding remarks 42
Basic methods and relevant examples 45
3 1 The Cole-Hopf transformation and the Burgers equation as a
paradigm 46
311* Exact solutions for a forced Burgers equation 50
3 2 Further application of the Cole-HopPtransformation 56
3 3 Method of piecewise linear approximation 60
331 Exact solution for a population with logistic growth 60
332 Exact solution for a population with a strong Allee ef-
fect 63
3 4 Exact solutipns of a generalized Fisher equation 68
341 Ansatz 69
342* The Ablowitz-Zeppetella method 71
3 5 More about ansatz 74
Single-species models 81
4 1 Impact of advection and migration 82
411 Advection 84
412 Density-dependent migration 85
413 General case 88
4 2 Accelerating population waves
421 Self-similar exact solution 93
4 3 The problem of critical aggregation 102
431 Practical stability concept 105
o
4432* The Wilhelmsson blow-up solution I l l
•( 5 Density-dependent diffusion 117
5 1 The Aronson-Newman solution and its generalization 117
511A general case 120
5 2 Stratified diffusion and the Allee effect 126
6 Models of interacting populations 137
6 1 Exact solution for a diffusive predator-prey system 137
611* Properties of the local system 140
612 Exact solution and its properties 143
613* Formal derivation of the exact solution 149
6 2 Migration waves in a resource-consumer system 154
7 Some alternative and complementary approaches 159
7 1 Wave speed and the eigenvalue problem 160
7 2 Convergence of the initial conditions 163
7 3 Convergence and the paradox of linearization 165
7 4 Application of the comparison principle 168
8 Ecological examples and applications 171
8 1 Invasion of Japanese beetle in the United States 172
8 2 Mount St Helens recolonization and the impact of predation 178
8 3 Stratified diffusion and rapid plant invasion 187
9 Appendix: Basic background mathematics 195
9 1 Ordinary differential equations and their solutions 195
9 2 Phase plane and stability analysis 198
9 3 Diffusion equation 200
References 205
Index 215
|
| adam_txt |
Chapman amp; Hall/CRC Mathematical Biology and Medicine Series
EXACTLY SOLVABLE MODELS
OF BIOLOGICAL INVASION
SERGEI V PETROVSKII AND BAI-LIAN LI
Chapman amp; Hall/CRC
Taylor amp; Francis Croup
Boca Raton London New York Singapore
Contents
Introduction 1
1 1 Why exactly solvable models are important 1
1 2 Intra- and inter-species interactions and local population dy-
namics 5
1 3 Basic mechanisms of species transport 11
1 4 Biological invasion: main facts and constituting examples 14
Models of biological invasion 17
2 1 Diffusion-reaction equations 17
2 2 Integral-difference models 24
2 3 Space-discrete models 30
2 4 Stochastic models 39
2 5 Concluding remarks 42
Basic methods and relevant examples 45
3 1 The Cole-Hopf transformation and the Burgers equation as a
paradigm 46
311* Exact solutions for a forced Burgers equation 50
3 2 Further application of the Cole-HopPtransformation 56
3 3 Method of piecewise linear approximation 60
331 Exact solution for a population with logistic growth 60
332 Exact solution for a population with a strong Allee ef-
fect 63
3 4 Exact solutipns'of a generalized Fisher equation 68
341 Ansatz 69
342* The Ablowitz-Zeppetella method 71
3 5 More about ansatz 74
Single-species models 81
4 1 Impact of advection and migration 82
411 Advection 84
412 Density-dependent migration 85
413 General case 88
4 2 Accelerating population waves
421 Self-similar exact solution 93
4 3 The problem of critical aggregation 102
431 Practical stability concept 105
o
4432* The Wilhelmsson blow-up solution I l l
•( 5 Density-dependent diffusion 117
5 1 The Aronson-Newman solution and its generalization 117
511A general case 120
5 2 Stratified diffusion and the Allee effect 126
6 Models of interacting populations 137
6 1 Exact solution for a diffusive predator-prey system 137
611* Properties of the local system 140
612 Exact solution and its properties 143
613* Formal derivation of the exact solution 149
6 2 Migration waves in a resource-consumer system 154
7 Some alternative and complementary approaches 159
7 1 Wave speed and the eigenvalue problem 160
7 2 Convergence of the initial conditions 163
7 3 Convergence and the paradox of linearization 165
7 4 Application of the comparison principle 168
8 Ecological examples and applications 171
8 1 Invasion of Japanese beetle in the United States 172
8 2 Mount St Helens recolonization and the impact of predation 178
8 3 Stratified diffusion and rapid plant invasion 187
9 Appendix: Basic background mathematics 195
9 1 Ordinary differential equations and their solutions 195
9 2 Phase plane and stability analysis 198
9 3 Diffusion equation 200
References 205
Index 215 |
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| discipline | Biologie |
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| language | English |
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| spelling | Petrovskii, Sergei V. Verfasser aut Exactly solvable models of biological invasion Sergei V. Petrovskii and Bai-Lian Li Boca Raton [u.a.] Chapman & Hall/CRC 2005 217 S. graph. Darst., Kt. 25cm txt rdacontent n rdamedia nc rdacarrier Chapman & Hall/CRC mathematical biology and medicine series Includes bibliographical references and index Mathematisches Modell Biological invasions Mathematical models Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Invasion Biologie (DE-588)4335542-0 gnd rswk-swf Invasion Biologie (DE-588)4335542-0 s Mathematisches Modell (DE-588)4114528-8 s b DE-604 Li, Bai-Lian Verfasser aut HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016388504&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Petrovskii, Sergei V. Li, Bai-Lian Exactly solvable models of biological invasion Mathematisches Modell Biological invasions Mathematical models Mathematisches Modell (DE-588)4114528-8 gnd Invasion Biologie (DE-588)4335542-0 gnd |
| subject_GND | (DE-588)4114528-8 (DE-588)4335542-0 |
| title | Exactly solvable models of biological invasion |
| title_auth | Exactly solvable models of biological invasion |
| title_exact_search | Exactly solvable models of biological invasion |
| title_exact_search_txtP | Exactly solvable models of biological invasion |
| title_full | Exactly solvable models of biological invasion Sergei V. Petrovskii and Bai-Lian Li |
| title_fullStr | Exactly solvable models of biological invasion Sergei V. Petrovskii and Bai-Lian Li |
| title_full_unstemmed | Exactly solvable models of biological invasion Sergei V. Petrovskii and Bai-Lian Li |
| title_short | Exactly solvable models of biological invasion |
| title_sort | exactly solvable models of biological invasion |
| topic | Mathematisches Modell Biological invasions Mathematical models Mathematisches Modell (DE-588)4114528-8 gnd Invasion Biologie (DE-588)4335542-0 gnd |
| topic_facet | Mathematisches Modell Biological invasions Mathematical models Invasion Biologie |
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