Nonlinear modeling of multistable perception

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Abstract
Multistable figures show that the stimulus-percept relation is not a single valued function. We therefore propose a tentative nonlinear model on the hypothesis that the graph of this relation is the equilibrium set of a dynamic system. For simplicity and to obtain testable predictions, we consider a system whose bifurcations are gradient-like and thus generically described by the elementary catastrophes. We motivate this general model, and then show how, in conjunction with the principle of minimal singularity, it implies cusp catastrophe geometry in a specific perceptual example. Indeed, we argue for canonical cusp geometry in this case. The model incorporates naturally certain observed features of multistable perception, such as hysteresis and bias effects. Despite being a continuum model it is naturally compatible with the subjective dichotomy of bistable perception. The model makes testable predictions which may easily be extended to other specific examples of multistable perception.

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