ANALOG STUDIES OF NONLINEAR-SYSTEMS

The design of analogue electronic experiments to investigate phenomena in nonlinear dynamics, especially stochastic phenomena, is described in practical terms. The advantages and disadvantages of this approach, in comparison to more conventional digital methods, are discussed. It is pointed out that analogue simulation provides a simple, inexpensiv e, technique that is easily applied in any laboratory to facilitate th e design and implementation of complicated and expensive experimental projects; and that there are some important problems for which analogu e methods have so far provided the only experimental approach. Applica tions to several topical problems are reviewed. Large rare fluctuation s are studied through measurements of the prehistory probability distr ibution, thereby testing for the first time some fundamental tenets of fluctuation theory. It has thus been shown for example that, whereas the fluctuations of equilibrium systems obey time-reversal symmetry, t hose under non-equilibrium conditions are temporally asymmetric. Stoch astic resonance, in which the signal-to-noise ratio for a weak periodi c signal in a nonlinear system can be enhanced by added noise, has bee n widely studied by analogue methods, and the main results are reviewe d; the closely related phenomena of noise-enhanced heterodyning and no ise-induced linearization are also described. Selected examples of the use of analogue methods for the study of transient phenomena in time- evolving systems are reviewed. Analogue experiments with quasimonochro matic noise, whose power spectral density is peaked. at some character istic frequency, have led to the discovery of a range of interesting a nd often counter-intuitive effects. These are reviewed and related to large fluctuation phenomena. Analogue studies of two examples of deter ministic nonlinear effects, modulation-induced negative differential r esistance (MINDR) and zero-dispersion nonlinear resonance (ZDNR) are d escribed. Finally, some speculative remarks about possible future dire ctions and applications of analogue experiments are discussed.