Nonlinearity, Chaos, and Complexity

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