Dynamical systems and population persistence
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Math. Soc.
2011
|
| Schriftenreihe: | Graduate studies in mathematics
118 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV026936328 | ||
| 003 | DE-604 | ||
| 005 | 20240513 | ||
| 007 | t| | ||
| 008 | 110326s2011 xx ad|| |||| 00||| eng d | ||
| 020 | |a 9780821849453 |c Hardcover |9 978-0-8218-4945-3 | ||
| 035 | |a (OCoLC)707161161 | ||
| 035 | |a (DE-599)HBZHT016707271 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-188 |a DE-355 |a DE-11 |a DE-91G | ||
| 084 | |a SK 810 |0 (DE-625)143257: |2 rvk | ||
| 084 | |a SK 950 |0 (DE-625)143273: |2 rvk | ||
| 084 | |a MAT 344 |2 stub | ||
| 100 | 1 | |a Smith, Hal L. |d 1947- |e Verfasser |0 (DE-588)111530326 |4 aut | |
| 245 | 1 | 0 | |a Dynamical systems and population persistence |c Hal L. Smith ; Horst R. Thieme |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 2011 | |
| 300 | |a XVII, 405 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Graduate studies in mathematics |v 118 | |
| 650 | 0 | 7 | |a Populationsbiologie |0 (DE-588)4046800-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Dynamisches System |0 (DE-588)4013396-5 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Dynamisches System |0 (DE-588)4013396-5 |D s |
| 689 | 0 | 1 | |a Populationsbiologie |0 (DE-588)4046800-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Thieme, Horst R. |d 1948- |e Verfasser |0 (DE-588)111523559 |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-4704-1180-0 |
| 830 | 0 | |a Graduate studies in mathematics |v 118 |w (DE-604)BV009739289 |9 118 | |
| 856 | 4 | 2 | |m HEBIS Datenaustausch |q application/pdf |u 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 |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-022457883 | |
Datensatz im Suchindex
| DE-BY-TUM_call_number | 0202 MAT 344 2024 B 921 |
|---|---|
| DE-BY-TUM_katkey | 2782585 |
| DE-BY-TUM_location | 02 |
| DE-BY-TUM_media_number | 040009557973 |
| _version_ | 1820894080566034432 |
| 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
|
| any_adam_object | 1 |
| author | Smith, Hal L. 1947- Thieme, Horst R. 1948- |
| author_GND | (DE-588)111530326 (DE-588)111523559 |
| author_facet | Smith, Hal L. 1947- Thieme, Horst R. 1948- |
| author_role | aut aut |
| author_sort | Smith, Hal L. 1947- |
| author_variant | h l s hl hls h r t hr hrt |
| building | Verbundindex |
| bvnumber | BV026936328 |
| classification_rvk | SK 810 SK 950 |
| classification_tum | MAT 344 |
| ctrlnum | (OCoLC)707161161 (DE-599)HBZHT016707271 |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01737nam a2200409 cb4500</leader><controlfield tag="001">BV026936328</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20240513 </controlfield><controlfield tag="007">t|</controlfield><controlfield tag="008">110326s2011 xx ad|| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780821849453</subfield><subfield code="c">Hardcover</subfield><subfield code="9">978-0-8218-4945-3</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)707161161</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)HBZHT016707271</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-188</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-91G</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 810</subfield><subfield code="0">(DE-625)143257:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 950</subfield><subfield code="0">(DE-625)143273:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 344</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Smith, Hal L.</subfield><subfield code="d">1947-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)111530326</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Dynamical systems and population persistence</subfield><subfield code="c">Hal L. Smith ; Horst R. Thieme</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Providence, RI</subfield><subfield code="b">American Math. Soc.</subfield><subfield code="c">2011</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XVII, 405 S.</subfield><subfield code="b">Ill., graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Graduate studies in mathematics</subfield><subfield code="v">118</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Populationsbiologie</subfield><subfield code="0">(DE-588)4046800-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Dynamisches System</subfield><subfield code="0">(DE-588)4013396-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Dynamisches System</subfield><subfield code="0">(DE-588)4013396-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Populationsbiologie</subfield><subfield code="0">(DE-588)4046800-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Thieme, Horst R.</subfield><subfield code="d">1948-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)111523559</subfield><subfield code="4">aut</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Online-Ausgabe</subfield><subfield code="z">978-1-4704-1180-0</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Graduate studies in mathematics</subfield><subfield code="v">118</subfield><subfield code="w">(DE-604)BV009739289</subfield><subfield code="9">118</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HEBIS Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">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</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-022457883</subfield></datafield></record></collection> |
| id | DE-604.BV026936328 |
| illustrated | Illustrated |
| indexdate | 2024-12-24T00:58:43Z |
| institution | BVB |
| isbn | 9780821849453 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-022457883 |
| oclc_num | 707161161 |
| open_access_boolean | |
| owner | DE-188 DE-355 DE-BY-UBR DE-11 DE-91G DE-BY-TUM |
| owner_facet | DE-188 DE-355 DE-BY-UBR DE-11 DE-91G DE-BY-TUM |
| physical | XVII, 405 S. Ill., graph. Darst. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Graduate studies in mathematics |
| series2 | Graduate studies in mathematics |
| spellingShingle | Smith, Hal L. 1947- Thieme, Horst R. 1948- Dynamical systems and population persistence Graduate studies in mathematics Populationsbiologie (DE-588)4046800-8 gnd Dynamisches System (DE-588)4013396-5 gnd |
| subject_GND | (DE-588)4046800-8 (DE-588)4013396-5 |
| 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 | Populationsbiologie (DE-588)4046800-8 gnd Dynamisches System (DE-588)4013396-5 gnd |
| topic_facet | Populationsbiologie Dynamisches System |
| 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 |
| volume_link | (DE-604)BV009739289 |
| work_keys_str_mv | AT smithhall dynamicalsystemsandpopulationpersistence AT thiemehorstr dynamicalsystemsandpopulationpersistence |