The invention relates to the management of eye rivalry, and by extension attentional rivalry, in a display system. The method includes the steps of determining visual environment parameters; determining a risk of visual suppression by ocular rivalry between an element of the visual environment and an element displayed by the display device as a function of the visual environment parameters; and according to the determined risk, to adjust the display. Developments of the invention describe the management of the luminance, of the chrominance and of the geometry of the displayed elements. Optimizations in the field of avionics are described. Software and system aspects are described (e.g. light sensors and / or gaze tracking, monocular type system).
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