It is possible that the work reported here, although appearing simple and obvious, has important consequences for those people who model real chaotic systems by computer simulation and by mathematical analysis, as well as for those people who construct electronic chaotic systems based on simulation and analysis. We have deliberately set out to build chaotic systems containing long chaotic transients, and noise-sensitive mappings. In the double-well oscillator [6] reported elsewhere, and also in the grazing bifurcations observed [7][8] in the offset impact oscillator [9], there are also intermittencies and regions of the motion which are strongly noise-dependent. It is even possible to see effects in the double-well oscillator strongly suggestive of trapping, with subsequent release by adding noise.
It is also possible to observe trapping in electromechanical chaotic toys which may be obtained commercially. In this case the motion may settle down into a periodic solution for some tens of minutes, from which it inevitably escapes eventually due to some local noise-like perturbation. Just as one cannot ever be sure that the chaotic transient has died away and the motion lies on the strange attractor, so in a trapping system one cannot be sure that the chaotic transient may not suddenly be re-excited by the interaction of a Feature with the system noise. In the electomechanical examples one may observe the system for some long time (hours or days) before finding a long-lived trapping event. If then the trapping lasts for some time there is a temptation to construct a mental model where there has been some physical change postulated to the physical configuration of the system.
The probabilities of entering and leaving a trap or snag
depend critically
the dimensionality of such systems. We have built a second-order
system from electronics.
In such a system it is possible to engineer a Feature
of relative lateral extent 
whose size compared with
the total available space for the system
is of the order of 
.
It is clear that whilst the time to capture
by the feature increases (as 
)
rapidly with the dimension N of the system,
the probability of release, set by the size of the
noise compared to delta, is largely independent of the
dimension. This means that capture can be an infrequent
occurrence in large-dimensional systems having traps which are
not small compared to the range of the variables. In such a system
there can be therefore a large amount of noise (commensurate with the
size of the feature) and the overall time development may be very
similar to that displayed in the figure.