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Foundations of Mathematical Biology
Supercellular Systems
- 1st Edition - January 1, 1973
- Editor: Robert J. Rosen
- Language: English
- Paperback ISBN:9 7 8 - 1 - 4 8 3 2 - 4 5 6 6 - 9
- Hardback ISBN:9 7 8 - 0 - 1 2 - 5 9 7 2 0 3 - 1
- eBook ISBN:9 7 8 - 1 - 4 8 3 2 - 7 1 8 5 - 9
Foundations of Mathematical Biology, Volume III, is devoted to the treatment of behavior of whole organisms and groups of organisms. The viewpoint taken throughout the book is a… Read more
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Request a sales quoteFoundations of Mathematical Biology, Volume III, is devoted to the treatment of behavior of whole organisms and groups of organisms. The viewpoint taken throughout the book is a holistic, phenomenological one. That is, the integrated behavior of these organisms and groups of organisms is not, in general, referred back to specific structural properties of interacting subunits (as in a reductionist scheme), but is rather treated on its own terms without invoking the properties of lower levels of organization. The book begins with an overview of organization and control in physiological systems, with emphasis on the mathematical techniques involved in more detailed investigations of specific physiological mechanisms. Separate chapters cover the cardiovascular system, with particular reference to blood flow; gross problems of organic form; a relational overview of physics, biology, and sociology; the automata theory in the context of the central nervous system; and populations of interacting organisms. The final chapter discusses the material presented in the entire work, some of its philosophical presuppositions and implications, and the possibility of constructing a unified theory of mathematical biology.
List of Contributors
Preface
Contents of Other Volumes
Chapter 1 Physiological Regulation and Control
I. Introduction
II. Mathematical Formulation of Systems
A. Some General Definitions
B. Assumptions
C. Description of Linear Systems
D. State Vector and State Equations
E. The Transfer Function and Its Properties
F. Vector Representation of Transfer Functions
G. Example: Electrical Phenomena across Excitable Membranes
III. Control Theory
A. Structure and Dynamics of Control Systems
B. Structure of Physiological Control
IV. Stability and Oscillations
A. Stability
B. Oscillations and Stability in Physiological Systems
V. Optimization
A. An Evolutionary Basis for Design and Operating Optimization
B. Hierarchical Aspects
C. Performance Indices, Cost Functions
D. Analytical Trade-off and Optimality Conditions
E. The Respiratory-Cardiovascular System
References
Chapter 2A Mathematical Aspects of Some Cardiovascular Phenomena
I. Introduction and Scope
II. Linear Case
III. Some Applications of the Linear Case: A Two-Chamber Theory
IV. Nonlinear Case
V. Applications of the Nonlinear Theory
VI. Volume Elasticity and the Elasticity of the Blood Vessel Wall:
Propagation of Pulse Waves
References
Chapter 2B The Principle of Adequate Design
I. Models and General Principles in Biology
II. Quantitative Description of a Form of an Organism
III. Form of Plants
IV. An Example of the Application to the External Shape of a Quadruped
V. Application to the Size of the Aorta
VI. Overall Design of the Circulatory System: Peripheral Resistance
VII. The Overall Design of the Cardiovascular System and the Evaluation
of Its Basic Parameters
References
Chapter 2C A Unified Approach to Physics, Biology, and Sociology
Chapter 3 Automata Theory in the Context of Theoretical Neurophysiology
I. The Concept of State
II. Finite-State Models of Neural Nets
III. Complexity Theory for Pattern Recognition Networks
IV. An Aside: Gödel's Incompleteness Theorem
V. From External to Internal Descriptions
VI. The Correction of Errors in Communication and Computation
A. Reliable Brains from Unreliable Neurons
B. Von Neumann's Multiplexing Scheme
C. Shannon's Communication Theory
D. Communication Theory and Automata
E. The Cowan-Winograd Theory of Reliable Automata
References
Chapter 4 The Deterministic Theory of Population Dynamics
I. Introduction
II. The Dynamics of an Isolated Species
A. Malthus' Equation
B. The Pearl-Verhulst Equation
C. A General Logistics Growth Rate Function
III. The Modes of Interaction between Two Species
A. Competition and Volterra's Competitive Exclusion Principle: Two
Species Competing for a Common Ecological Niche
B. Two Species Living in a Predator-Prey Relationship
C. Symbiosis
D. Parasitism
E. A General Qualitative Theory for the Interactions between Two
Species
IV. The Interactions between Three or More Species
A. Competition Involving Several Species
B. Predation Involving Several Species
V. Incorporation of "Historical Actions"
A. The System Equations for Predation
B. Law of Conservation of the Means and Law of Perturbation of the
Means for "Historical Actions"
VI. Epilogue
References
Chapter 5 Is There a Unified Mathematical Biology?
Author Index
Subject Index, Volume I
Subject Index, Volume II
Subject Index, Volume III
- No. of pages: 430
- Language: English
- Edition: 1
- Published: January 1, 1973
- Imprint: Academic Press
- Paperback ISBN: 9781483245669
- Hardback ISBN: 9780125972031
- eBook ISBN: 9781483271859
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