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Abstract. An algorithm which can be realized by synergetic systems and which was introduced by one of us (Haken 1987) for the recognition of patterns is extended so that the perception of ambiguous patterns can be modelled. In this approach so-called attention parameters are subjected to a damping mechanism mimicking the effect of saturation of attention. In this way oscillations of perception arise quite naturally. Our approach takes also ambiguous patterns with bias into account which leads to different periods of the attention paid to the one or the other interpretation of the pattern. Our results are in good agreement with previous psycho-physical studies by other authors. Finally we show how hysteresis of perception can be modelled.

The recognition of ambiguous patterns by humans is modelled by coupled differential equations which describe the formation of percepts by means of order parameters which in turn are determined by the saturation of attention parameters. We study the impact of fluctuations on the attention parameters and thus indirectly on the recognition of ambiguous patterns. Excellent agreement with psychophysical experimental results by Price on the transient behaviour of switching times and by Borsellino et al. on the distribution function of switching times as function of the size of the visual field is obtained. Our model allows us to deal also with the shift of width and position of the distribution function with respect to slow and fast observers in the sense of Borsellino.

When the same syllable is presented repeatedly to a human subject, it undergoes perceptual changes known as verbal transformations. However, the dynamics of such perceptual changes is poorly understood. In the present work we show that the main organization of the perceptual transitions is into pairs. This pairwise coupling is pronounced in the frequency of switching to pair members, but not in their dwell times (the time spent perceiving a given phonemic form before switching to another form). We show that the paircoupled transforms of perception have a faster and more stable dynamic than the nonpaircoupled transforms. We also demonstrate that the pairwise coupling is stronger than would be expected from random arrangement of small numbers of transforms. These characteristic patterns of verbal transforms have been predicted by a mathematical model, first proposed as a model of perceptual alternations of ambiguous visual figures.

The propagation of material interfaces is investigated under the action of a localized moving source which deposits or removes material. Among others the latter process applies to beam cutting techniques. We develop a Kuramoto-Sivashinsky-type model and find a new type of ripple forming mechanism. This theory offers a new explanation for the occurrence of striation patterns which often degrade the quality of cutting edges.