Three Chaotic Systems
Robert C. Hilborn · 2000
Abstract This chapter introduces chaotic behaviour by examining three systems — an electronic circuit, an iterated map model (the logistic map), and a set of differential equations (the Lorenz model) — and their behaviour in state space (phase space). Bifurcations are introduced as changes in dynamical behaviour as parameters describing the systems are changed. Similar features such as period-doubling are demonstrated. The chapter also introduces the basic vocabulary needed to describe nonlinear behaviour. The distinction between linear behaviour and nonlinear behaviour is emphasized. Chaotic behaviour provides a new paradigm to explain complex behaviour and the implications of this new paradigm are discussed, including the loss of predictability for chaotic systems even though their underlying mathematical descriptions are deterministic. Bifurcation diagrams and attractors provide powerful visual presentations of how behaviour changes as parameters are varied.