Strange attractors in a multisector business cycle model

“Chaos” in futures markets? A nonlinear dynamical analysis

“…Empirical applications of nonlinear dynamical analysis techniques in economics are few in number. They are concentrated in two areas: assessments of the business cycle [Brock and Sayers (1988); Day (1983); Lorenz (1987)l and financial markets [Hinich and Patterson (1985); Savit (1989); Scheinkman and LeBaron (1989); van 'For example, "Can nonlinear dynamics explain speculative bubbles?" or "Do trading rules, such as those imposed on futures markets, create price patterns similar to patterns generated by 'strange attractors' (defined in the next section)?"…”

“…In practice, some economists argue that separating deterministic and stochastic processes may be very difficult due to the "noisy" nature of economic data [Mirowski (1990)l. Although applications of chaos analysis in economics are still very rare [examples include Baumol and Benhabib; Brock (1986); Brock and Sayers (1988); Candela and Gardini (1986); Day (1983); Goodwin (1990); Lorenz (1987); Melese and Transue (1986)], there may be potential for its use in some markets.…”

Homoclinic tangles in a Kaldor-like business cycle model

“…This model was criticized because of its lack of microfoundation, and today it appears very simple and rather dated if compared with the modern approaches to the business cycle. However, since the reformulation of the Kaldor model as a continuous time dynamical system proposed by Chang and Smyth (1971), this model has been generating a considerable amount of economic, pedagogical and methodological interest, both in its continuous-time and discrete-time versions (see, e.g., Varian, 1979;Dana and Malgrange, 1984;Herrmann, 1985;Gabisch and Lorenz, 1989;Lorenz, 1987Lorenz, , 1992Lorenz, , 1993Grasman and Wentzel, 1994;Dohtani et al, 1996;.…”

Phase-Locking in a Goodwin Model

“…Many economic phenomena can be thought of as coupled oscillators. Examples are the interaction between seasonal fluctuations and the business cycle, the interaction between different sectors in an economy (Lorenz, 1987a), and the interaction between different national or regional economies (Lorenz, 1987b).We consider the simplest case of coupled oscillators, namely a model that consists of an independent oscillator which acts as a forcing on an internally generated cyclic motion. The internal motion is produced by a Goodwin model of economic business cycles (Goodwin, 1951).…”