Reaction-diffusion equations and their applications to biology
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| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London u.a.
Acad. Press
1986
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| Online-Zugang: | Inhaltsverzeichnis |
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| 100 | 1 | |a Britton, N. F. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Reaction-diffusion equations and their applications to biology |
| 264 | 1 | |a London u.a. |b Acad. Press |c 1986 | |
| 300 | |a IX, 277 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Biomathématiques | |
| 650 | 7 | |a Biomathématiques |2 ram | |
| 650 | 7 | |a Equations de réaction - Diffusion |2 ram | |
| 650 | 4 | |a Équations aux dérivées partielles | |
| 650 | 4 | |a Équations de réaction-diffusion | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Biology | |
| 650 | 4 | |a Biomathematics | |
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Reaction-diffusion equations | |
| 650 | 0 | 7 | |a Reaktions-Diffusionsgleichung |0 (DE-588)4323967-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Partielle Differentialgleichung |0 (DE-588)4044779-0 |2 gnd |9 rswk-swf |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-000446709 | |
Datensatz im Suchindex
| DE-BY-TUM_call_number | 0202 BIO 105 2002 A 1574 |
|---|---|
| DE-BY-TUM_katkey | 82490 |
| DE-BY-TUM_location | 02 |
| DE-BY-TUM_media_number | 040020653781 |
| _version_ | 1820805299752140800 |
| adam_text | Contents
Preface v
1. Introduction 1
1.1 Derivation of the Equations 1
1.2 Stochastic Effects 3
2. Systems of Ordinary Differential Equations 5
2.1 Preliminaries 5
2.2 Systems of Linear Ordinary Differential Equations 7
2.3 Systems of Nonlinear Ordinary Differential Equations 10
2.4 Asymptotic Behaviour of Second-Order Systems 11
2.5 Limit Cycles in Systems of Order Greater than Two:
The Oregonator 14
3. Conservative Systems 17
3.1 Introduction 17
3.2 The Lotka-Volterra System 17
3.3 Conservative Reaction-Diffusion Systems 21
3.4 Conservative Systems in Epidemiology 23
4. The Scalar Reaction-Diffusion Equation 29
4.1 Introduction 29
4.2 The Maximum Principle and Comparison Theorems 32
4.3 Existence and Uniqueness of Solutions 35
4.4 Stationary Solutions and Asymptotic Behaviour for the Neumann
and Cauchy Problems 39
4.5 Stationary Solutions and Asymptotic Behaviour for the Dirichlet
Problem: The Spruce Budworm Model 47
4.6 Travelling Wave Fronts 61
4.7 Global Stability of Travelling Wave Fronts 70
5. Analytic Techniques for Systems of Parabolic Partial Differential
Equations 73
5.1 Introduction 73
5.2 Comparison Theorems 75
5.3 Invariant Sets 79
viii Contents
5.4 Nested Rectangles and Time-dependent Comparison Functions . . 85
5.5 The Cauchy Problem and Fundamental Solutions 92
5.6 Stationary Solutions and Their Stability 96
5.7 The Energy Method 101
6. Bifurcation Theory 109
6.1 Introduction 109
6.2 Bifurcation in One Dimension 110
6.3 Questions of Stability: The One-dimensional Case 114
6.4 Bifurcation in m Dimensions and in Infinite Dimensions .... 119
6.5 Bifurcation of Steady Solutions from Real Simple Eigenvalues . . 121
6.6 Stability of the Bifurcating Solutions: The Factorisation Theorem . 125
6.7 Bifurcation Analysis in a Finite One-dimensional Domain .... 127
6.8 Bifurcation in a Finite Two-dimensional Domain: A Model for
Hydranth Regeneration in Tubularia 133
6.9 The Hopf Bifurcation 138
6.10 Stability of the Bifurcating Branches: The Factorisation Theorem
for the Hopf Bifurcation 145
6.11 An Example of the Hopf Bifurcation in Two Dimensions .... 150
6.12 The Hopf Bifurcation in m Dimensions and in Infinite Dimensions. 154
6.13 Plane-wave Solutions of Reaction-Diffusion Equations 159
7. Asymptotic Methods for Oscillatory Systems 163
7.1 Introduction 163
7.2 Regular and Singular Perturbations 165
7.3 Perturbations of the Harmonic Oscillator 166
7.4 Failure of the Regular Perturbation Scheme 168
7.5 The Method of Renormalisation 170
7.6 The Two-timing Method 174
7.7 The Two-timing Method for Reaction-Diffusion Systems .... 183
7.8 Averaging Methods 185
7.9 The Krylov-Bogoliubov-Mitropolsky Method 187
7.10 Averaging Methods for Reaction-Diffusion Systems 190
7.11 Perturbations of Strongly Nonlinear Oscillatory Systems 191
7.12 The Hopf Bifurcation and A-O Systems 195
8. Singular Perturbations 201
8.1 Introduction 201
8.2 Michaelis-Menten Theory 202
8.3 Neglect of the Fast Variable Derivative Term 208
8.4 Threshold Phenomena 210
8.5 Singular Perturbation Analysis of a Threshold Phenomenon . . . 212
8.6 Solitary Travelling Waves: The Leading Wave Front 220
8.7 Solitary Travelling Waves: Behaviour before the Formation of the
Trailing Wave Front 222
Contents ix
8.8 Solitary Travelling Waves: Formation and Development of the
Trailing Wave Front 224
8.9 Systems with Solitary Travelling Waves 235
8.9.1 The Cyclic AMP Control System in Dictyostelium
Discoldeum 235
8.9.2 The Belousov-Zhabotinskii Reaction 236
8.9.3 The Fitzhugh-Nagumo Equations 237
9. Macromolecular Carriers: Asymptotic Techniques 239
9.1 Introduction 239
9.2 Macromolecular Carriers 239
9.3 Facilitation of Oxygen Diffusion into Muscle by Myoglobin . . . 240
9.4 Carbon Monoxide Poisoning 247
References 259
Index 273
|
| any_adam_object | 1 |
| author | Britton, N. F. |
| author_facet | Britton, N. F. |
| author_role | aut |
| author_sort | Britton, N. F. |
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| callnumber-first | Q - Science |
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| callnumber-raw | QH323.5 |
| callnumber-search | QH323.5 |
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| callnumber-subject | QH - Natural History and Biology |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.3/53 |
| dewey-search | 515.3/53 |
| dewey-sort | 3515.3 253 |
| dewey-tens | 510 - Mathematics |
| discipline | Biologie Mathematik |
| format | Book |
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| id | DE-604.BV000714917 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-23T10:02:20Z |
| institution | BVB |
| isbn | 0121351408 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000446709 |
| oclc_num | 12135642 |
| open_access_boolean | |
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| owner_facet | DE-12 DE-91G DE-BY-TUM DE-739 DE-29T DE-188 DE-11 |
| physical | IX, 277 S. |
| publishDate | 1986 |
| publishDateSearch | 1986 |
| publishDateSort | 1986 |
| publisher | Acad. Press |
| record_format | marc |
| spellingShingle | Britton, N. F. Reaction-diffusion equations and their applications to biology Biomathématiques Biomathématiques ram Equations de réaction - Diffusion ram Équations aux dérivées partielles Équations de réaction-diffusion Mathematik Biology Biomathematics Mathematics Reaction-diffusion equations Reaktions-Diffusionsgleichung (DE-588)4323967-5 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Biologie (DE-588)4006851-1 gnd |
| subject_GND | (DE-588)4323967-5 (DE-588)4044779-0 (DE-588)4006851-1 |
| title | Reaction-diffusion equations and their applications to biology |
| title_auth | Reaction-diffusion equations and their applications to biology |
| title_exact_search | Reaction-diffusion equations and their applications to biology |
| title_full | Reaction-diffusion equations and their applications to biology |
| title_fullStr | Reaction-diffusion equations and their applications to biology |
| title_full_unstemmed | Reaction-diffusion equations and their applications to biology |
| title_short | Reaction-diffusion equations and their applications to biology |
| title_sort | reaction diffusion equations and their applications to biology |
| topic | Biomathématiques Biomathématiques ram Equations de réaction - Diffusion ram Équations aux dérivées partielles Équations de réaction-diffusion Mathematik Biology Biomathematics Mathematics Reaction-diffusion equations Reaktions-Diffusionsgleichung (DE-588)4323967-5 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Biologie (DE-588)4006851-1 gnd |
| topic_facet | Biomathématiques Equations de réaction - Diffusion Équations aux dérivées partielles Équations de réaction-diffusion Mathematik Biology Biomathematics Mathematics Reaction-diffusion equations Reaktions-Diffusionsgleichung Partielle Differentialgleichung Biologie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000446709&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT brittonnf reactiondiffusionequationsandtheirapplicationstobiology |