Dynamic models and control of biological systems:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht [u.a.]
Springer
2009
|
| Series: | Biomedicine
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 275 S. graph. Darst. 235 mm x 155 mm |
| ISBN: | 9781441903594 9781441903587 |
Staff View
MARC
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| 100 | 1 | |a Rao, Vadrevu Sree Hari |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Dynamic models and control of biological systems |c Vadrevu Sree Hari Rao ; Ponnada Raja Sekhara Rao |
| 264 | 1 | |a Dordrecht [u.a.] |b Springer |c 2009 | |
| 300 | |a XIII, 275 S. |b graph. Darst. |c 235 mm x 155 mm | ||
| 336 | |b txt |2 rdacontent | ||
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| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Biological systems |x Mathematical models | |
| 650 | 4 | |a Biometry |x methods | |
| 650 | 4 | |a Chemostat | |
| 650 | 4 | |a Microbial populations |x Mathematical models | |
| 650 | 4 | |a Microbiological Processes | |
| 650 | 4 | |a Models, Biological | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-017612347 | ||
Record in the Search Index
| _version_ | 1804139203669262336 |
|---|---|
| adam_text | Contents
1
Basic
Models
................................................................. 1
1.1
Introduction
............................................................ 1
1.2
Biological Principles
.................................................. 3
1.3
Formulation of the Mathematical Model
............................. 4
1.4
Properties of Solutions
................................................ 5
1.5
Equilibrium Solutions
................................................. 7
1.6
Stability Analysis
...................................................... 8
1.7
General Uptake Function
............................................. 18
1.8
Discussion
............................................................. 24
1.9
Notes and Remarks
.................................................... 24
1.10
Exercises
............................................................... 25
2
Chemostat Versus the Lake
................................................. 27
2.1
Introduction
............................................................ 27
2.2
Models Involving Time Delays
....................................... 28
2.3
Time Delay Models in Growth Response
............................ 31
2.3.1
Global Stability
.............................................. 35
2.3.2
A Modified Model
........................................... 39
2.4
Material Recycling with and without Time Delays
.................. 41
2.4.1
Finite Delays in Material Recycling
........................ 42
2.4.2
Distributed Delays
........................................... 46
2.5
A More Realistic Model
.............................................. 64
2.5.1
Qualitative Properties of Solutions
......................... 65
2.5.2
Local Stability
............................................... 72
2.5.3
Global Asymptotic Stability Results
........................ 80
2.6
Discussion
............................................................. 89
2.7
Notes and Remarks
.................................................... 90
2.8
Exercises
............................................................... 91
3
Instability Tendencies
....................................................... 93
3.1
Introduction
............................................................ 93
3.2
Instability Tendencies
................................................. 94
3.3
Instability Characteristics of Model
.................................. 100
Contents
3.4
Equilibria and Instability
.............................................. 106
3.5
Biocontrol Mechanisms
............................................... 112
3.6
Discussion
............................................................. 114
3.7
Notes and Remarks
....................................................
Π
4
3.8
Exercises
...............................................................
Π5
Self-Regulation
............................................................... 117
4.1
Introduction
............................................................ 117
4.2
Qualitative Properties of Solutions
................................... 119
4.3
Persistence of Solutions
............................................... 125
4.4
Global Asymptotic Stability Results
................................. 128
4.5
Oscillations and the Self-regulation
.................................. 143
4.5.1
Properties of Solutions
...................................... 144
4.5.2
Existence of Periodic Solutions
............................. 146
4.6
A Model with Discrete Delay in Growth Response
................. 156
4.6.1
Stability Results
............................................. 156
4.7
Discussion
............................................................. 170
4.8
Notes and Remarks
.................................................... 170
4.9
Exercises
............................................................... 172
Wall Growth
.................................................................. 175
5.1
Introduction
............................................................ 175
5.2
Basic Properties of Solutions
......................................... 176
5.3
Global Dynamics
...................................................... 180
5.4
Discussion
............................................................. 186
5.5
Notes and Remarks
.................................................... 187
5.6
Exercises
............................................................... 187
Zones of No Activation
...................................................... 189
6.1
Introduction
............................................................ 189
6.2
Global Stability for the System
....................................... 190
6.3
Global Stability with Self-regulation and Zones
..................... 195
6.4
Discussion
............................................................. 203
6.5
Notes and Remarks
.................................................... 204
6.6
Exercises
............................................................... 205
Influence of the Control Mechanisms
..................................... 207
7.1
Introduction
............................................................ 207
7.2
Stability Under Self-Regulatory Control Mechanism
............... 207
7.3
Stability Under Wall Growth Mechanism
............................ 212
7.4
Stability Under Zones of No Activation
.............................. 221
7.5
Discussion
............................................................. 224
7.6
Notes and Remarks
.................................................... 225
7.7
Exercises
............................................................... 226
Contents xiii
8 Parameter
Estimation
Using Dynamic Optimization
.................... 227
8.1
Introduction
............................................................ 227
8.2
Dynamic Optimization
................................................ 228
8.3
Application to Basic Chemostat Model
.............................. 231
8.4
Method of Differential Transforms
................................... 236
8.4.1
Estimation of Washout Rate
D
.............................. 240
8.5
Discussion
............................................................. 247
8.6
Notes and Comments
................................................. 247
8.7
Exercises
............................................................... 247
A Derivatives and Definitions
................................................. 249
В
Results on Boundedness and Convergence
............................... 251
С
Uniqueness and Stability
.................................................... 255
References
......................................................................... 263
Author Index
...................................................................... 269
Subject Index
..................................................................... 271
|
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| author | Rao, Vadrevu Sree Hari Rao, Ponnada Raja Sekhara |
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| classification_rvk | WC 7000 WI 1500 |
| ctrlnum | (OCoLC)419644697 (DE-599)DNB992871298 |
| dewey-full | 571.15195 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 571 - Physiology & related subjects |
| dewey-raw | 571.15195 |
| dewey-search | 571.15195 |
| dewey-sort | 3571.15195 |
| dewey-tens | 570 - Biology |
| discipline | Biologie |
| format | Book |
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| id | DE-604.BV035556544 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:40:21Z |
| institution | BVB |
| isbn | 9781441903594 9781441903587 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017612347 |
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| owner_facet | DE-355 DE-BY-UBR DE-11 DE-83 |
| physical | XIII, 275 S. graph. Darst. 235 mm x 155 mm |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Springer |
| record_format | marc |
| series2 | Biomedicine |
| spelling | Rao, Vadrevu Sree Hari Verfasser aut Dynamic models and control of biological systems Vadrevu Sree Hari Rao ; Ponnada Raja Sekhara Rao Dordrecht [u.a.] Springer 2009 XIII, 275 S. graph. Darst. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Biomedicine Mathematisches Modell Biological systems Mathematical models Biometry methods Chemostat Microbial populations Mathematical models Microbiological Processes Models, Biological Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Mikrobielles Wachstum (DE-588)4422344-4 gnd rswk-swf Mikrobielles Wachstum (DE-588)4422344-4 s Mathematisches Modell (DE-588)4114528-8 s b DE-604 Rao, Ponnada Raja Sekhara Verfasser aut Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017612347&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rao, Vadrevu Sree Hari Rao, Ponnada Raja Sekhara Dynamic models and control of biological systems Mathematisches Modell Biological systems Mathematical models Biometry methods Chemostat Microbial populations Mathematical models Microbiological Processes Models, Biological Mathematisches Modell (DE-588)4114528-8 gnd Mikrobielles Wachstum (DE-588)4422344-4 gnd |
| subject_GND | (DE-588)4114528-8 (DE-588)4422344-4 |
| title | Dynamic models and control of biological systems |
| title_auth | Dynamic models and control of biological systems |
| title_exact_search | Dynamic models and control of biological systems |
| title_full | Dynamic models and control of biological systems Vadrevu Sree Hari Rao ; Ponnada Raja Sekhara Rao |
| title_fullStr | Dynamic models and control of biological systems Vadrevu Sree Hari Rao ; Ponnada Raja Sekhara Rao |
| title_full_unstemmed | Dynamic models and control of biological systems Vadrevu Sree Hari Rao ; Ponnada Raja Sekhara Rao |
| title_short | Dynamic models and control of biological systems |
| title_sort | dynamic models and control of biological systems |
| topic | Mathematisches Modell Biological systems Mathematical models Biometry methods Chemostat Microbial populations Mathematical models Microbiological Processes Models, Biological Mathematisches Modell (DE-588)4114528-8 gnd Mikrobielles Wachstum (DE-588)4422344-4 gnd |
| topic_facet | Mathematisches Modell Biological systems Mathematical models Biometry methods Chemostat Microbial populations Mathematical models Microbiological Processes Models, Biological Mikrobielles Wachstum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017612347&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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