This paper is concerned with the behaviour of simple low-dimensional non-linear mappings under iteration. The mappings are designed to contain small Features which we can call traps [1] or snags. These are distinguished by the following behaviours: If the state variable enters a trap feature the chaotic [2][3] motion ceases (in the absence of noise) and the system rests at a fixed point. If the state variable enters a snag, the motion is confined to the region of the snag but may continue to develop with iteration number, possibly periodically or chaotically. In the absence of noise the state variable remains within the trap or within the snag feature, unless the snag has a structure which can eject the motion beyond the adjacent fixed point which defines the extent of the feature.
The dynamics of these systems display bursty behaviour which is reminiscent of intermittency, and may reasonably be thought of as intermittent. In the presence of added noise, or if the snag has stucture extending beyond the feature, the state vector may be ejected from the feature until it is recaptured some variable time later. The statistics are well-defined and accessible to calculation.
In practical systems rather than mathematical idealisations or simulations there will always be added unavoidable system noise. This may lead to grossly qualitative different behaviours for the real system compared to its simulation or theoretical behaviour.
This has important consequences for general large scale simulations of non-linear complex systems having some kind of feedback or global search process. In cases where the simulation displays erratic or bursty behaviour, it would be reasonable to search for traps or snags.
We also observe experimentally that interesting behaviours occur when the features are of a size such that the inherent system noise can perturb the motion beyond the extent of the feature. For simulation purposes, such added noise may be approximated by adding together a set of computed random variables which mimic the presence of additive white Gaussian noise.
We shall give some simple results on the theoretical statistics of the distribution of the probability of entering and leaving a trap as a function of the number of iterations.
We shall show some experiments which confirm the predicted behaviour, which is reminsicent of burst noise and is also reminiscent of intermittency of the Pomeau-Manneville [4][5] types. Not all systems which appear to be intermittent may be behaving according to the known classes of intermittency. It may be that noise driven processes appear very similar to such intermittencies.