Monotone random systems theory and applications:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong ; London
Springer
2002
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| Series: | Lecture notes in mathematics
1779 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 234 S. |
| ISBN: | 3540432469 |
Staff View
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| 100 | 1 | |a Čuešov, Igor' D. |d 1951- |e Verfasser |0 (DE-588)118042750 |4 aut | |
| 245 | 1 | 0 | |a Monotone random systems theory and applications |c Igor Chueshov |
| 264 | 1 | |a Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong ; London |b Springer |c 2002 | |
| 300 | |a VIII, 234 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 1779 | |
| 650 | 4 | |a Differentiable dynamical systems | |
| 650 | 4 | |a Ergodic theory | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Introduction 1
1. General Facts about Random Dynamical Systems 9
1.1 Metric Dynamical Systems 9
1.2 Concept of RDS 13
1.3 Random Sets 18
1.4 Dissipative, Compact and Asymptotically Compact RDS .... 24
1.5 Trajectories 32
1.6 Omega limit Sets 34
1.7 Equilibria 38
1.8 Random Attractors 41
1.9 Dissipative Linear and Affine RDS 45
1.10 Connection Between Attractors and Invariant Measures 49
2. Generation of Random Dynamical Systems 55
2.1 RDS Generated by Random Differential Equations 55
2.2 Deterministic Invariant Sets 61
2.3 The Ito and Stratonovich Stochastic Integrals 65
2.4 RDS Generated by Stochastic Differential Equations 70
2.5 Relations Between RDE and SDE 76
3. Order Preserving Random Dynamical Systems 83
3.1 Partially Ordered Banach Spaces 83
3.2 Random Sets in Partially Ordered Spaces 88
3.3 Definition of Order Preserving RDS 93
3.4 Sub Equilibria and Super Equilibria 95
3.5 Equilibria 100
3.6 Properties of Invariant Sets of Order Preserving RDS 105
3.7 Comparison Principle 109
4. Sublinear Random Dynamical Systems 113
4.1 Sublinear and Concave RDS 113
4.2 Equilibria and Semi Equilibria for Sublinear RDS 116
4.3 Almost Equilibria 122
VIII Contents
4.4 Limit Set Trichotomy for Sublinear RDS 125
4.5 Random Mappings 132
4.6 Positive Affine RDS 138
5. Cooperative Random Differential Equations 143
5.1 Basic Assumptions and the Existence Theorem 143
5.2 Generation of RDS 145
5.3 Random Comparison Principle 150
5.4 Equilibria, Semi Equilibria and Attractors 156
5.5 Random Equations with Concavity Properties 160
5.6 One Dimensional Explicitly Solvable Random Equations 166
5.7 Applications 171
5.7.1 Random Biochemical Control Circuit 171
5.7.2 Random Gonorrhea Model 175
5.7.3 Random Model of Symbiotic Interaction 176
5.7.4 Random Gross Substitute System 178
5.8 Order Preserving RDE with Non Standard Cone 180
6. Cooperative Stochastic Differential Equations 185
6.1 Main Assumptions 185
6.2 Generation of Order Preserving RDS 186
6.3 Conjugacy with Random Differential Equations 188
6.4 Stochastic Comparison Principle 192
6.5 Equilibria and Attractors 194
6.6 One Dimensional Stochastic Equations 199
6.6.1 Stochastic Equations on K+ 199
6.6.2 Stochastic Equations on a Bounded Interval 206
6.7 Stochastic Equations with Concavity Properties 214
6.8 Applications 219
6.8.1 Stochastic Biochemical Control Circuit 219
6.8.2 Stochastic Gonorrhea Model 221
6.8.3 Stochastic Model of Symbiotic Interaction 222
6.8.4 Lattice Models of Statistical Mechanics 223
References 227
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| any_adam_object | 1 |
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| author_variant | i d č id idč |
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| ctrlnum | (OCoLC)471625078 (DE-599)BVBBV014214171 |
| dewey-full | 519.23 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.23 |
| dewey-search | 519.23 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV014214171 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:59:45Z |
| institution | BVB |
| isbn | 3540432469 |
| language | English |
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| physical | VIII, 234 S. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Čuešov, Igor' D. 1951- Verfasser (DE-588)118042750 aut Monotone random systems theory and applications Igor Chueshov Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong ; London Springer 2002 VIII, 234 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1779 Differentiable dynamical systems Ergodic theory Stochastic processes Zufälliges dynamisches System (DE-588)4335207-8 gnd rswk-swf Zufälliges dynamisches System (DE-588)4335207-8 s DE-604 Lecture notes in mathematics 1779 (DE-604)BV000676446 1779 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009745946&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Čuešov, Igor' D. 1951- Monotone random systems theory and applications Lecture notes in mathematics Differentiable dynamical systems Ergodic theory Stochastic processes Zufälliges dynamisches System (DE-588)4335207-8 gnd |
| subject_GND | (DE-588)4335207-8 |
| title | Monotone random systems theory and applications |
| title_auth | Monotone random systems theory and applications |
| title_exact_search | Monotone random systems theory and applications |
| title_full | Monotone random systems theory and applications Igor Chueshov |
| title_fullStr | Monotone random systems theory and applications Igor Chueshov |
| title_full_unstemmed | Monotone random systems theory and applications Igor Chueshov |
| title_short | Monotone random systems theory and applications |
| title_sort | monotone random systems theory and applications |
| topic | Differentiable dynamical systems Ergodic theory Stochastic processes Zufälliges dynamisches System (DE-588)4335207-8 gnd |
| topic_facet | Differentiable dynamical systems Ergodic theory Stochastic processes Zufälliges dynamisches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009745946&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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