Mathematical biology:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1993
|
| Edition: | 2., corr. ed. |
| Series: | Biomathematics
19 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 723 - 743 Später mehrbd. begrenztes Werk |
| Physical Description: | XIV, 767 S. Ill., graph. Darst. |
| ISBN: | 354057204X 038757204X |
Staff View
MARC
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| 100 | 1 | |a Murray, James D. |d 1931- |e Verfasser |0 (DE-588)129898708 |4 aut | |
| 245 | 1 | 0 | |a Mathematical biology |c J. D. Murray |
| 250 | |a 2., corr. ed. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1993 | |
| 300 | |a XIV, 767 S. |b Ill., graph. Darst. | ||
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| 490 | 1 | |a Biomathematics |v 19 | |
| 500 | |a Literaturverz. S. 723 - 743 | ||
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Record in the Search Index
| _version_ | 1804123215027503104 |
|---|---|
| adam_text | Table of Contents
1. Continuous Population Models for Single Species 1
1.1 Continuous Growth Models 1
1.2 Insect Outbreak Model: Spruce Budworm 4
1.3 Delay Models 8
1.4 Linear Analysis of Delay Population Models: Periodic Solutions 12
1.5 Delay Models in Physiology: Dynamic Diseases 15
1.6 Harvesting a Single Natural Population 24
*1.7 Population Model with Age Distribution 29
Exercises 33
2. Discrete Population Models for a Single Species 36
2.1 Introduction: Simple Models 36
2.2 Cobwebbing: A Graphical Procedure of Solution 38
2.3 Discrete Logistic Model: Chaos 41
2.4 Stability, Periodic Solutions and Bifurcations 47
2.5 Discrete Delay Models 51
2.6 Fishery Management Model 54
2.7 Ecological Implications and Caveats 57
Exercises 59
3. Continuous Models for Interacting Populations 63
3.1 Predator Prey Models: Lotka Volterra Systems 63
3.2 Complexity and Stability 68
3.3 Realistic Predator Prey Models 70
3.4 Analysis of a Predator Prey Model with Limit Cycle Periodic
Behaviour: Parameter Domains of Stability 72
3.5 Competition Models: Principle of Competitive Exclusion ... 78
3.6 Mutualism or Symbiosis 83
3.7 General Models and Some General and Cautionary Remarks . 85
3.8 Threshold Phenomena 89
Exercises 92
* Denotes sections in which the mathematics is at a higher level. These sections can
be omitted without loss of continuity.
X Table of Contents
4. Discrete Growth Models for Interacting Populations 95
4.1 Predator Prey Models: Detailed Analysis 96
*4.2 Synchronized Insect Emergence: 13 Year Locusts 100
4.3 Biological Pest Control: General Remarks 106
Exercises 107
5. Reaction Kinetics 109
5.1 Enzyme Kinetics: Basic Enzyme Reaction 109
5.2 Michaelis Menten Theory: Detailed Analysis and the
Pseudo Steady State Hypothesis HI
5.3 Cooperative Phenomena 118
5.4 Autocatalysis, Activation and Inhibition 122
5.5 Multiple Steady States, Mushrooms and Isolas 130
Exercises 137
6. Biological Oscillators and Switches 140
6.1 Motivation, History and Background 140
6.2 Feedback Control Mechanisms 143
6.3 Oscillations and Switches Involving Two or More Species:
General Qualitative Results 148
6.4 Simple Two Species Oscillators: Parameter Domain
Determination for Oscillations 156
6.5 Hodgkin Huxley Theory of Nerve Membranes:
FitzHugh Nagumo Model 161
6.6 Modelling the Control of Testosterone Secretion 166
Exercises 175
7. Belousov Zhabotinskii Reaction 1^9
7.1 Belousov Reaction and the Field Noyes (FN) Model 179
7.2 Linear Stability Analysis of the FN Model and Existence
of Limit Cycle Solutions 183
7.3 Non local Stability of the FN Model 187
7.4 Relaxation Oscillators: Approximation for the
Belousov Zhabotinskii Reaction 190
7.5 Analysis of a Relaxation Model for Limit Cycle Oscillations
in the Belousov Zhabotinskii Reaction 192
Exercises 199
8. Perturbed and Coupled Oscillators and Black Holes 200
8.1 Phase Resetting in Oscillators 200
8.2 Phase Resetting Curves 204
8.3 Black Holes 208
8.4 Black Holes in Real Biological Oscillators 21°
8.5 Coupled Oscillators: Motivation and Model System 2^
Table of Contents XI
*8.6 Singular Perturbation Analysis: Preliminary Transformation . 217
*8.7 Singular Perturbation Analysis: Transformed System .... 220
*8.8 Singular perturbation Analysis: Two Time Expansion .... 223
*8.9 Analysis of the Phase Shift Equation and Application
to Coupled Belousov Zhabotinskii Reactions 227
Exercises 231
9. Reaction Diffusion, Chemotaxis and Non local Mechanisms . . . 232
9.1 Simple Random Walk Derivation of the Diffusion Equation . . 232
9.2 Reaction Diffusion Equations 236
9.3 Models for Insect Dispersal 238
9.4 Chemotaxis 241
*9.5 Non local Effects and Long Range Diffusion 244
*9.6 Cell Potential and Energy Approach to Diffusion 249
Exercises 252
10. Oscillator Generated Wave Phenomena and Central Pattern
Generators 254
10.1 Kinematic Waves in the Belousov Zhabotinskii Reaction . . . 254
10.2 Central Pattern Generator: Experimental Facts in the
Swimming of Fish 258
*10.3 Mathematical Model for the Central Pattern Generator . . . 261
*10.4 Analysis of the Phase Coupled Model System 268
Exercises 273
11. Biological Waves: Single Species Models 274
11.1 Background and the Travelling Wave Form 274
11.2 Fisher Equation and Propagating Wave Solutions 277
11.3 Asymptotic Solution and Stability of Wavefront Solutions
of the Fisher Equation 281
11.4 Density Dependent Diffusion Reaction Diffusion Models
and Some Exact Solutions 286
11.5 Waves in Models with Multi Steady State Kinetics:
The Spread and Control of an Insect Population 297
11.6 Calcium Waves on Amphibian Eggs: Activation Waves
on Medaka Eggs 305
Exercises 309
12. Biological Waves: Multi species Reaction Diffusion Models .... 311
12.1 Intuitive Expectations 311
12.2 Waves of Pursuit and Evasion in Predator Prey Systems . . . 315
12.3 Travelling Fronts in the Belousov Zhabotinskii Reaction . . . 322
12.4 Waves in Excitable Media 328
XII Table of Contents
12.5 Travelling Wave Trains in Reaction Diffusion Systems
with Oscillatory Kinetics 336
*12.6 Linear Stability of Wave Train Solutions of X ui Systems . . . 340
12.7 Spiral Waves 343
*12.8 Spiral Wave Solutions of A w Reaction Diffusion Systems . . . 350
Exercises 356
*13. Travelling Waves in Reaction Diffusion Systems with
Weak Diffusion: Analytical Techniques and Results 360
*13.1 Reaction Diffusion System with Limit Cycle Kinetics and
Weak Diffusion: Model and Transformed System 360
*13.2 Singular Perturbation Analysis: The Phase Satisfies
Burgers Equation 363
*13.3 Travelling Wavetrain Solutions for Reaction Diffusion Systems
with Limit Cycle Kinetics and Weak Diffusion: Comparison
with Experiment 367
14. Spatial Pattern Formation with Reaction/Population Interaction
Diffusion Mechanisms 372
14.1 Role of Pattern in Developmental Biology 372
14.2 Reaction Diffusion (Turing) Mechanisms 375
14.3 Linear Stability Analysis and Evolution of Spatial Pattern:
General Conditions for Diffusion Driven Instability 380
14.4 Detailed Analysis of Pattern Initiation in a Reaction Diffusion
Mechanism 387
14.5 Dispersion Relation, Turing Space, Scale and Geometry Effects
in Pattern Formation in Morphogenetic Models 397
14.6 Mode Selection and the Dispersion Relation 408
14.7 Pattern Generation with Single Species Models:
Spatial Heterogeneity with the Spruce Budworm Model . . . 414
14.8 Spatial Patterns in Scalar Population Interaction Reaction
Diffusion Equations with Convection: Ecological Control
Strategies 419
*14.9 Nonexistence of Spatial Patterns in Reaction Diffusion
Systems: General and Particular Results 424
Exercises 430
15. Animal Coat Patterns and Other Practical Applications
of Reaction Diffusion Mechanisms 435
15.1 Mammalian Coat Patterns How the Leopard Got Its Spots . 436
15.2 A Pattern Formation Mechanism for Butterfly Wing Patterns . 448
15.3 Modelling Hair Patterns in a Whorl in Acetabularia 468
Table of Contents XIII
16. Neural Models of Pattern Formation 481
16.1 Spatial Patterning in Neural Firing with a Simple
Activation Inhibition Model 481
16.2 A Mechanism for Stripe Formation in the Visual Cortex . . . 489
16.3 A Model for the Brain Mechanism Underlying Visual
Hallucination Patterns 494
16.4 Neural Activity Model for Shell Patterns 505
Exercises 523
17. Mechanical Models for Generating Pattern and Form
in Development 525
17.1 Introduction and Background Biology 525
17.2 Mechanical Model for Mesenchymal Morphogenesis 528
17.3 Linear Analysis, Dispersion Relation and Pattern Formation
Potential 538
17.4 Simple Mechanical Models Which Generate Spatial Patterns
with Complex Dispersion Relations 542
17.5 Periodic Patterns of Feather Germs 554
17.6 Cartilage Condensations in Limb Morphogenesis 558
17.7 Mechanochemical Model for the Epidermis 566
17.8 Travelling Wave Solutions of the Cytogel Model 572
17.9 Formation of Microvilli 579
17.10 Other Applications of Mechanochemical Models 586
Exercises 590
18. Evolution and Developmental Programmes 593
18.1 Evolution and Morphogenesis 593
18.2 Evolution and Morphogenetic Rules in Cartilage Formation
in the Vertebrate Limb 599
18.3 Developmental Constraints, Morphogenetic Rules and
the Consequences for Evolution 606
19. Epidemic Models and the Dynamics of Infectious Diseases .... 610
19.1 Simple Epidemic Models and Practical Applications 611
19.2 Modelling Venereal Diseases 619
19.3 Multi group Model for Gonorrhea and Its Control 623
19.4 AIDS: Modelling the Transmission Dynamics of the Human
Immunodeficiency Virus (HIV) 624
19.5 Modelling the Population Dynamics of Acquired Immunity
to Parasite Infection 630
*19.6 Age Dependent Epidemic Model and Threshold Criterion . . 640
19.7 Simple Drug Use Epidemic Model and Threshold Analysis . . 645
Exercises 649
XIV Table of Contents
20. Geographic Spread of Epidemics 651
20.1 Simple Model for the Spatial Spread of an Epidemic .... 651
20.2 Spread of the Black Death in Europe 1347 1350 655
20.3 The Spatial Spread of Rabies Among Foxes I: Background
and Simple Model 659
20.4 The Spatial Spread of Rabies Among Foxes II: Three Species
(SIR) Model 666
20.5 Control Strategy Based on Wave Propagation into a
Non epidemic Region: Estimate of Width of a Rabies Barrier . 681
20.6 Two Dimensional Epizootic Fronts and Effects of Variable
Fox Densities: Quantitative Predictions for a Rabies Outbreak
in England 689
Exercises 696
Appendices 697
1. Phase Plane Analysis 697
2. Routh Hurwitz Conditions, Jury Conditions, Descartes Rule
of Signs and Exact Solutions of a Cubic 702
3. Hopf Bifurcation Theorem and Limit Cycles 706
4. General Results for the Laplacian Operator in Bounded
Domains 720
Bibliography 723
Index 745
|
| any_adam_object | 1 |
| author | Murray, James D. 1931- |
| author_GND | (DE-588)129898708 |
| author_facet | Murray, James D. 1931- |
| author_role | aut |
| author_sort | Murray, James D. 1931- |
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| bvnumber | BV008860898 |
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| ctrlnum | (OCoLC)246602081 (DE-599)BVBBV008860898 |
| dewey-full | 570.1511822 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 570 - Biology |
| dewey-raw | 570.1511822 |
| dewey-search | 570.1511822 |
| dewey-sort | 3570.1511822 |
| dewey-tens | 570 - Biology |
| discipline | Biologie Mathematik |
| edition | 2., corr. ed. |
| format | Book |
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| id | DE-604.BV008860898 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:26:13Z |
| institution | BVB |
| isbn | 354057204X 038757204X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005860477 |
| oclc_num | 246602081 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-M49 DE-BY-TUM DE-384 DE-92 DE-20 DE-703 DE-19 DE-BY-UBM DE-29 DE-634 DE-83 DE-188 |
| owner_facet | DE-91G DE-BY-TUM DE-M49 DE-BY-TUM DE-384 DE-92 DE-20 DE-703 DE-19 DE-BY-UBM DE-29 DE-634 DE-83 DE-188 |
| physical | XIV, 767 S. Ill., graph. Darst. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Springer |
| record_format | marc |
| series | Biomathematics |
| series2 | Biomathematics |
| spelling | Murray, James D. 1931- Verfasser (DE-588)129898708 aut Mathematical biology J. D. Murray 2., corr. ed. Berlin [u.a.] Springer 1993 XIV, 767 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Biomathematics 19 Literaturverz. S. 723 - 743 Später mehrbd. begrenztes Werk Mathematics cabt Biologia - modelli matematici sbt Biomathematik Mathematik Biomathematik (DE-588)4139408-2 gnd rswk-swf Biologie (DE-588)4006851-1 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Biomathematik (DE-588)4139408-2 s DE-604 Biologie (DE-588)4006851-1 s Mathematisches Modell (DE-588)4114528-8 s 1\p DE-604 Biomathematics 19 (DE-604)BV000894631 19 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005860477&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Murray, James D. 1931- Mathematical biology Biomathematics Mathematics cabt Biologia - modelli matematici sbt Biomathematik Mathematik Biomathematik (DE-588)4139408-2 gnd Biologie (DE-588)4006851-1 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| subject_GND | (DE-588)4139408-2 (DE-588)4006851-1 (DE-588)4114528-8 |
| title | Mathematical biology |
| title_auth | Mathematical biology |
| title_exact_search | Mathematical biology |
| title_full | Mathematical biology J. D. Murray |
| title_fullStr | Mathematical biology J. D. Murray |
| title_full_unstemmed | Mathematical biology J. D. Murray |
| title_short | Mathematical biology |
| title_sort | mathematical biology |
| topic | Mathematics cabt Biologia - modelli matematici sbt Biomathematik Mathematik Biomathematik (DE-588)4139408-2 gnd Biologie (DE-588)4006851-1 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| topic_facet | Mathematics Biologia - modelli matematici Biomathematik Mathematik Biologie Mathematisches Modell |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005860477&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000894631 |
| work_keys_str_mv | AT murrayjamesd mathematicalbiology |