320 pages, 64 line figures
Covering a broad range of topics, this text provides a comprehensive survey of the modelling of chaotic dynamics and complexity in the natural and social sciences. Its attention to models in both the physical and social sciences and the detailed philosophical approach make this an unique text in the midst of many current books on chaos and complexity.
Part 1 deals with the mathematical model as an instrument of investigation. The general meaning of modelling and, more specifically, questions concerning linear modelling are discussed. Part 2 deals with the theme of chaos and the origin of chaotic dynamics. Part 3 deals with the theme of complexity: a property of the systems and of their models which is intermediate between stability and chaos.
Including an extensive index and bibliography along with numerous examples and simplified models, this is an ideal course text.
...the book will certainly bring a lot of pleasure to the reader with philosophical inclinations EMS Newsletter
CONTENTS; PREFACE; PART I: LINEAR AND NONLINEAR PROCESSES; 1.1 Introduction; 1.2 Modelling; 1.3 The Origins of System Dynamics: Mechanics; 1.4 Linearity in Models; 1.5 One of The Most Basic Natural Systems: The Pendulum; 1.6 Linearity as a First, Often Insufficient Approximation; 1.7 The Nonlinearity of Natural Processes: The Case of The Pendulum; 1.8 Dynamical Systems and The Phase Space; 1.9 Extension of The Concepts and Models Used in Physics to Economics; 1.10 The Chaotic Pendulum; 1.11 Linear Models in Social Processes: The Case of Two Interacting Populations; 1.12 Nonlinear Models in Social Processes: The Model of Volterra-Lotka and Some of Its Variants in Ecology; 1.13 Nonlinear Models in Social Processes: The Volterra-Lotka Model Applied to Urban and Regional Science; PART II: FROM NONLINEARITY TO CHAOS; 2.1 Introduction; 2.2 Dynamical Systems and Chaos; 2.3 Strange and Chaotic Attractors; 2.4 Chaos in Real Systems and in Mathematical Models; 2.5 Stability in Dynamical Systems; 2.6 The Problem of Measuring Chaos in Real Systems; 2.7 Logistic Growth as A Population Development Model; 2.8 A Nonlinear Discrete Model: The Logistic Map; 2.9 The Logistic Map: Some Results of Numerical Simulations and An Application; 2.10 Chaos in Systems: The Main Concepts; PART III: COMPLEXITY; 3.1 Introduction; 3.2 Inadequacy of Reductionism; 3.3 Some Aspects of The Classical Vision of Science; 3.4 From Determinism to Complexity: Self-Organisation, A New Understanding of System Dynamics; 3.5 What is Complexity?; 3.6 Complexity and Evolution; 3.7 Complexity in Economic Processes; 3.8 Some Thoughts on The Meaning of 'Doing Mathematics'; 3.9 Digression into The Main Interpretations of The Foundations of Mathematics; 3.10 The Need for A Mathematics of (or for) Complexity; REFERENCES; NAME INDEX; SUBJECT INDEX
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