Dynamical system theory in biology: 1 Stability theory and its applications
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Wiley
1970
|
| Series: | Wiley interscience series on biomedical engineering
|
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 302 S. graph. Darst. |
| ISBN: | 0471735507 |
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| 245 | 1 | 0 | |a Dynamical system theory in biology |n 1 |p Stability theory and its applications |c Robert Rosen |
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Record in the Search Index
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| adam_text | Contents
1 THE BASIC CONCEPTS OF DYNAMICAL SYSTEM THEORY 1
1.1 Dynamical Systems in Euclidean Space 1
1.2 Nonautonomous Systems 16
1.3 Parameters in Dynamical Systems: Forcing Functions 18
2 DYNAMICAL SYSTEMS IN PHYSICS AND BIOLOGY 23
2.1 Classical Newtonian Systems 23
2.2 Conservative Systems 36
2.3 Volterra Systems 41
2.4 Chemical and Biochemical Kinetic Systems 45
2.5 Analogous Systems and Analogies 52
3 STABILITY IN DYNAMICAL SYSTEMS 59
3.1 Stability: Basic Concepts 59
3.2 The Stability of Critical Points 66
3.3 Criteria for the Stability of Critical Points of Autonomous Systems:
Lyapunov Functions 70
3.4 Asymptotic Stability of Critical Points: Some Heuristic Consider¬
ations 79
3.5 Stability under Change of Variables 81
3.6 Structural Stability 83
4 INTRODUCTION TO LINEAR DYNAMICAL SYSTEMS 88
4.1 Linearization around Critical Points 88
4.2 Review of Linear Algebra 91
ix
x Contents
4.3 General Solution of the ^ Dimensional Linear Homogeneous Dy¬
namical System 100
4.4 Two Dimensional Linear Homogeneous Systems 104
4.5 Homogeneous Linear Systems with Zero Eigenvalues; Closed
Systems 111
5 QUALITATIVE THEORY OF NONLINEAR DYNAMICAL SYSTEMS:
POINCARE BENDIXON THEORY 117
5.1 The Linearization Theorem 117
5.2 Applications of the Linearization Theorem 125
5.3 Van der Pol s Equation and Limit Cycles 131
5.4 Closed Trajectories; the Index of a Closed Curve 139
5.5 The Poincare—Bendixon Theorem 146
5.6 Activation and Inhibition in Dynamical Systems 151
6 INTRODUCTION TO NONAUTONOMOUS SYSTEMS 161
6.1 Nonautonomous Linear Homogeneous Dynamical Systems 161
6.2 Nonautonomous Linear Nonhomogeneous Dynamical Systems 168
6.3 Some Special Cases 173
7 DYNAMICAL ASPECTS OF MORPHOGENESIS 180
7.1 Introduction 180
7.2 Morphogenesis: The Rashevsky Turing Theory 180
7.3 Open Systems as Morphogenetic Metaphors 190
7.4 Multiple Steady States in Open Systems 195
7.5 Some Historical Considerations on Cellular Biochemistry 202
7.6 Inhibition, Induction, and Repression in Catalyzed Open Systems
208
7.7 Some Specific Realizations of Cellular Dynamical Metaphors 211
8 DYNAMICAL ASPECTS OF EXCITATION 224
8.1 Introduction 224
8.2 Abstract Two Factor Elements 224
8.3 Realizations of Two Factor Elements 232
8.4 Networks of Two Factor Elements and Their Realizations 237
8.5 General Two Factor Reaction Diffusion Schemes 247
8.6 Other Dynamical Metaphors for Nerve Excitation 251
Dynamical Systems xi
9 THE FORMALISM OF STATISTICAL MECHANICS 265
9.1 Introduction 265
9.2 Flows on Phase Space 266
9.3 Liouville s Theorem 268
9.4 Another Formulation of Liouville s Theorem 272
9.5 Time and Phase Averages of Observables along Trajectories; Ergo
dicity and the Ergodic Hypothesis 276
9.6 Quasi Ergodicity in Conservative Systems 280
9.7 Some Applications of the Statistical Mechanical Formalism to Bio¬
logical Dynamics 284
INDEX 297
|
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| discipline | Biologie |
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| id | DE-604.BV002321765 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:43:55Z |
| institution | BVB |
| isbn | 0471735507 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001521703 |
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| physical | XI, 302 S. graph. Darst. |
| publishDate | 1970 |
| publishDateSearch | 1970 |
| publishDateSort | 1970 |
| publisher | Wiley |
| record_format | marc |
| series2 | Wiley interscience series on biomedical engineering |
| spelling | Rosen, Robert 1934-1998 Verfasser (DE-588)133687929 aut Dynamical system theory in biology 1 Stability theory and its applications Robert Rosen New York [u.a.] Wiley 1970 XI, 302 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley interscience series on biomedical engineering (DE-604)BV002321764 1 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001521703&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rosen, Robert 1934-1998 Dynamical system theory in biology |
| title | Dynamical system theory in biology |
| title_auth | Dynamical system theory in biology |
| title_exact_search | Dynamical system theory in biology |
| title_full | Dynamical system theory in biology 1 Stability theory and its applications Robert Rosen |
| title_fullStr | Dynamical system theory in biology 1 Stability theory and its applications Robert Rosen |
| title_full_unstemmed | Dynamical system theory in biology 1 Stability theory and its applications Robert Rosen |
| title_short | Dynamical system theory in biology |
| title_sort | dynamical system theory in biology stability theory and its applications |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001521703&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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