The concept of trapping seems to have applications in informing thought about complex chaotic systems. First, trapping happens suddenly with no warning. Second, in a high dimensional system it can happen with small probability per iteration but relative ultimate certainty even though the system is noisy. Third, it gives insight into bursty behaviour that is not necessarily linked to classical intermittencies. In figure 7 we show these effects in the simulation of a double potential well [7,8] system; the system consists of a resonant circuit or a linear spring-mass arrangement with two separated centres, and is closely related to impacting systems. Further interesting phenomena suggestive of chaotic trapping are to be found in the paper [9] on spatio-temporal chaos of Eilbeck and Scott.
Figure 7: Trapping in a double well oscillator
It is possible to construct relatively simple electronic circuits to study these trapping effects empirically. The behaviour of such circuits is striking; the possible types of behaviour become much more vivid when observed directly than they are in thought experiments or simulations.
Of great importance to modern technology is the likely behaviour of large arrays of parallel computing processes. With a single computer, a crash is usually fatal until human intervention restores the operation. In a large network of computers, an individual crash may cause the network to respond by resetting the computer at that node. The question arises as to the reliability of such a system. It is possible that the study of trapping non-linear systems may inform this kind of engineering.