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