Dynamical systems and population persistence:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Math. Soc.
2011
|
| Series: | Graduate studies in mathematics
118 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 405 S. Ill., graph. Darst. |
| ISBN: | 9780821849453 |
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MARC
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| 245 | 1 | 0 | |a Dynamical systems and population persistence |c Hal L. Smith ; Horst R. Thieme |
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Record in the Search Index
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| adam_text |
Dynamical Systems
and Population
Persistence
Hal L Smith
Horst R Thieme
Graduate Studies
in Mathematics
Volume 118
American Mathematical Society
Providence, Rhode Island
Contents
Preface ix
Introduction 1
Chapter 1 Semiflows on Metric Spaces 9
§1 1 Metric spaces 9
§1 2 Semiflows 17
§1 3 Invariant sets 19
§1 4 Exercises 25
Chapter 2 Compact Attractors 29
§2 1 Compact attractors of individual sets 30
§2 2 Compact attractors of classes of sets 36
§2 3 A sufficient condition for asymptotic smoothness 51
§2 4 a-limit sets of total trajectories 52
§2 5 Invariant sets identified through Lyapunov functions 52
§2 6 Discrete semiflows induced by weak contractions 54
§2 7 Exercises 57
Chapter 3 Uniform Weak Persistence 61
§3 1 Persistence definitions 61
§3 2 An SEIRS epidemic model in patchy host populations 64
§3 3 Nonlinear matrix models: Prolog 71
§3 4 The May-Leonard example of cyclic competition 78
53 5 Exercises 84
vi Contents
Chapter 4 Uniform Persistence 87
§4 1 From uniform weak to uniform persistence 87
§4 2 From uniform weak to uniform persistence: Discrete case 91
§4 3 Application to a metered endemic model of SIR type 94
§4 4 From uniform weak to uniform persistence for time-set E + 97
§4 5 Persistence a la Baron von Miinchhausen 99
§4 6 Navigating between alternative persistence functions 107
§4 7 A fertility reducing endemic with two stages of infection 110
§4 8 Exercises 123
Chapter 5 The Interplay of Attractors, Repellers, and Persistence 125
§5 1 An attractor of points facilitates persistence 125
§5 2 Partition of the global attractor under uniform persistence 127
§5 3 Repellers and dual attractors 135
§5 4 The cyclic competition model of May and Leonard revisited 139
§5 5 Attractors at the brink of extinction 140
§5 6 An attractor under two persistence functions 141
§5 7 Persistence of bacteria and phages in a chemostat 142
§5 8 Exercises 155
Chapter 6 Existence of Nontrivial Fixed Points via Persistence 157
§6 1 Nontrivial fixed points in the global compact attractor 158
§6 2 Periodic solutions of the Lotka-Volterra predator-prey model 160
§6 3 Exercises 162
Chapter 7 Nonlinear Matrix Models: Main Act 163
§7 1 Forward invariant balls and compact attractors of bounded
sets 163
§7 2 Existence of nontrivial fixed points 165
§7 3 Uniform persistence and persistence attractors 167
§7 4 Stage persistence 171
§7 5 Exercises 175
Chapter 8 Topological Approaches to Persistence 177
§8 1 Attractors and repellers 177
§8 2 Chain transitivity and the Butler-McGehee lemma 180
§8 3 Acyclicity implies uniform weak persistence 185
§8 4 Uniform persistence in a food chain 191
Contents vii
§8 5 The metered endemic model revisited 196
§8 6 Nonlinear matrix models (epilog): Biennials 199
§8 7 An endemic with vaccination and temporary immunity 209
§8 8 Lyapunov exponents and persistence for ODEs and maps 215
§8 9 Exercises 229
Chapter 9 An SI Endemic Model with Variable Infectivity 231
§9 1 The model 231
§9 2 Host persistence and disease extinction 236
§9 3 Uniform weak disease persistence 237
§9 4 The semiflow - 239
§9 5 Existence of a global compact attractor 240
§9 6 Uniform disease persistence 245
§9 7 Disease extinction and the disease-free equilibrium 247
§9 8 The endemic equilibrium 249
§9 9 Persistence as a crossroad to global stability 250
§9 10 Measure-valued distributions of infection-age 254
Chapter 10 Semiflows Induced by Semilinear Cauchy Problems 261
§10 1 Classical, integral, and mild solutions 261
§10 2 Semiflow via Lipschitz condition and contraction principle 265
§10 3 Compactness all the way 266
§10 4 Total trajectories 271
§10 5 Positive solutions: The low road 273
§10 6 Heterogeneous time-autonomous boundary conditions 279
Chapter 11 Microbial Growth in a Tubular Bioreactor 283
§11 1 Model description 283
§11 2 The no-bacteria invariant set 287
§11 3 The solution semiflow 291
§11 4 Bounds on solutions and the global attractor 292
§11 5 Stability of the washout equilibrium 296
§11 6 Persistence of the microbial population 301
§11 7 Exercises 304
Chapter 12 Dividing Cells in a Chemostat 307
§12 1 An integral equation 309
§12 2 A Co-semigroup ' 314
viii Contents
§12 3 A semilinear Cauchy problem 318
§12 4 Extinction and weak persistence via Laplace transform 320
§12 5 Exercises 325
Chapter 13 Persistence for Nonautonomous Dynamical Systems 327
§13 1 The simple chemostat with time-dependent washout rate 327
§13 2 General time-heterogeneity 332
§13 3 Periodic and asymptotically periodic semiflows 335
§13 4 Uniform persistence of the cell population 336
§13 5 Exercises 339
Chapter 14 Forced Persistence in Linear Cauchy Problems 341
§14 1 Uniform weak persistence and asymptotic Abel-averages 342
§14 2 A compact attracting set 343
§14 3 Uniform persistence in ordered Banach space 344
Chapter 15 Persistence via Average Lyapunov Functions 349
§15 1 Weak average Lyapunov functions 350
§15 2 Strong average Lyapunov functions 354
§15 3 The time-heterogeneous hypercycle equation 355
§15 4 Exercises 361
Appendix A Tools from Analysis and Differential Equations 363
§A l Lower one-sided derivatives 363
§A 2 Absolutely continuous functions 364
§A 3 The method of fluctuation 365
§A 4 Differential inequalities and positivity of solutions 367
§A 5 Perron-Frobenius theory 372
§A 6 Exercises 375
Appendix B Tools from Functional Analysis and Integral Equations 377
§B l Compact sets in Z7(R+) 377
§B 2 Volterra integral equations 378
§B 3 Fourier transform methods for integro-differential equations 380
§B 4 Closed linear operators 385
§B 5 Exercises 390
Bibliography 391
Index , 403 |
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| physical | XVII, 405 S. Ill., graph. Darst. |
| publishDate | 2011 |
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| spelling | Smith, Hal L. 1947- Verfasser (DE-588)111530326 aut Dynamical systems and population persistence Hal L. Smith ; Horst R. Thieme Providence, RI American Math. Soc. 2011 XVII, 405 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics 118 Dynamisches System (DE-588)4013396-5 gnd rswk-swf Populationsbiologie (DE-588)4046800-8 gnd rswk-swf Dynamisches System (DE-588)4013396-5 s Populationsbiologie (DE-588)4046800-8 s DE-604 Thieme, Horst R. 1948- Verfasser (DE-588)111523559 aut Erscheint auch als Online-Ausgabe 978-1-4704-1180-0 Graduate studies in mathematics 118 (DE-604)BV009739289 118 HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022457883&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Smith, Hal L. 1947- Thieme, Horst R. 1948- Dynamical systems and population persistence Graduate studies in mathematics Dynamisches System (DE-588)4013396-5 gnd Populationsbiologie (DE-588)4046800-8 gnd |
| subject_GND | (DE-588)4013396-5 (DE-588)4046800-8 |
| title | Dynamical systems and population persistence |
| title_auth | Dynamical systems and population persistence |
| title_exact_search | Dynamical systems and population persistence |
| title_full | Dynamical systems and population persistence Hal L. Smith ; Horst R. Thieme |
| title_fullStr | Dynamical systems and population persistence Hal L. Smith ; Horst R. Thieme |
| title_full_unstemmed | Dynamical systems and population persistence Hal L. Smith ; Horst R. Thieme |
| title_short | Dynamical systems and population persistence |
| title_sort | dynamical systems and population persistence |
| topic | Dynamisches System (DE-588)4013396-5 gnd Populationsbiologie (DE-588)4046800-8 gnd |
| topic_facet | Dynamisches System Populationsbiologie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022457883&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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