ISBN:
9780080369648
Language:
English
Pages:
Online-Ressource (343 p)
Edition:
Online-Ausg.
Series Statement:
IFSR International Series on Systems Science and Engineering
Parallel Title:
Print version Foundations of Mathematical System Dynamics : The Fundamental Theory of Causal Recursion and Its Application to Social Science and Economics
DDC:
301
Keywords:
Electronic books
Abstract:
This book is a foundational study of causality as conceived in the mathematical sciences. It is shown that modern mathematical dynamics involves a formulation of the fundamental concept of causality, and an exhaustive classification of causal systems. Among them are the 'self-steering' and 'self-regulating' systems, which together form the class of purposive systems, on whose specific properties the book then focuses. These properties are the mathematical-dynamical foundations of the behavioural and social sciences. This is the definitive book on causality and purposive processes by the origin
Description / Table of Contents:
Front Cover; Foundations of Mathematical System Dynamics: The Fundamental Theory of Causal Recursion and its Application to Social Science and Economics; Copyright Page; Table of Contents; Preface; Part 1: Fundamental Dynamics: The General Theory of Causal Recursion; CHAPTER 1. Causal Recursion in Theoretical Physics; 1.1 Causal Relation, Causal Law, and Causal Recursion; 1.2. Causal Recursion in Classical Physics: the Hamiltonian Formalism; 1.3 Causal Recursion in Quantum Physics: the Unitary Timetranslations in a Hubert Space of States
Description / Table of Contents:
1.4 The Molecular State-description: a Third Level of Causal Recursion1.5 Conservative and Dissipative Systems; CHAPTER 2. Causal Recursion in Mathematical Dynamics; 2.1. Causal Recursion in Dynamical Systems Generally; 2.2 Dynamical Systems With Nilpotent Causal Recursion; 2.3. Dynamical Systems with Full Causal Recursion; 2.4. Self-organization vs Rigid-structured Dynamical Systems; 2.5 Causality, Determinism, and Indeterminism; CHAPTER 3. The Systematics of Goal-directed Systems; 3.1. General properties of the goals of self-regulating systems; 3.2. Self-regulating equilibrium systems
Description / Table of Contents:
3.3. Periodically pulsating self-regulating systems3.4. Almost periodically pulsating self-regulating systems; 3.5. Irregularly ('chaotically') pulsating self-regulating systems; 3.6. Self-steering systems; 3.7. The Ashby-Lange effect; 3.8. Systems that are steerable from outside; 3.9. Finite systems and Turing machines; CHAPTER 4. The Modes of Asymptotic Approach of Goals; 4.1. Causal Suction: The Ideal Type; 4.2. The Generalization of Causal Suction to ç Dimensions and to Nonlinear Causal Recursions in an Equilibrium System; 4.3. The Generalization of Causal Suction t o Nonequilibrium Goals
Description / Table of Contents:
4.4. Causal Torsion4.5. Causal Vortex; 4.6. The Approach of a Goal Through Rapid Vibrations; 4.7. The Degeneracies of Causal Suction, Torsion, and Vortex, and of Rapid Vibrations, into Satellites and Comets; 4.8. The General Connection Between Linear Difference and Differential Equations; CHAPTER 5. The Variety of Dynamical Systems Generated by a Single Nonlinear Map (An Example); 5.1. The Séparatrices and Regions; 5.2. The Special Points; 5.3. Structural Stability and Instability; 5.4. Hopf Bifurcation: an Algorithm for the Detection of its Existence
Description / Table of Contents:
Part 2: Simple Applications: Causal Recursion in Population Dynamics and Economic Growth TheoryCHAPTER 6. Verhulstian Ecosystems and the Feigenbaum Bifurcations of their Equilibrium States; 6.1. The Verhulst Axioms; 6.2. The Preliminary (Local) Stability Analysis; 6.3. Verhulstian Ecosystems as Self-regulating Equilibrium Systems: a Small or Medium Total Biomass; 6.4 Verhulstian Ecosystems as Periodically Pulsating Self-regulating Systems of Period 2: a Large Total Biomass but a Small Death Rate
Description / Table of Contents:
6.5. The Feigenbaum Bifurcations and their Interruptions in Verhulstian Ecosystems in the General Case: a Large Death Rate and Total Biomass
Note:
Description based upon print version of record
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