title: Bifurcation analysis applied to a model of motion integration with a multistable stimulus.
abstract: A computational study into the motion perception dynamics of a multistable psychophysics stimulus is presented. A diagonally drifting grating viewed through a square aperture is perceived as moving in the actual grating direction or in line with the aperture edges (horizontally or vertically). The different percepts are the product of interplay between ambiguous contour cues and specific terminator cues. We present a dynamical model of motion integration that performs direction selection for such a stimulus and link the different percepts to coexisting steady states of the underlying equations. We apply the powerful tools of bifurcation analysis and numerical continuation to study changes to the model's solution structure under the variation of parameters. Indeed, we apply these tools in a systematic way, taking into account biological and mathematical constraints, in order to fix model parameters. A region of parameter space is identified for which the model reproduces the qualitative behaviour observed in experiments. The temporal dynamics of motion integration are studied within this region; specifically, the effect of varying the stimulus gain is studied, which allows for qualitative predictions to be made.
authors.affiliation: Neuromathcomp Project Team, INRIA Sophia Antipolis Méditerranée, 2004 Route des Lucioles-BP 93, 06902 Sophia Antipolis, France. james.rankin@inria.fr
authors.forename: James
authors.initials: J
authors.lastname: Rankin
authors.forename: Emilien
authors.initials: E
authors.lastname: Tlapale
authors.forename: Romain
authors.initials: R
authors.lastname: Veltz
authors.forename: Olivier
authors.initials: O
authors.lastname: Faugeras
authors.forename: Pierre
authors.initials: P
authors.lastname: Kornprobst
mesh_terms: D003198:Computer Simulation; D006801:Humans; D008954:Models, Biological; D008962:Models, Theoretical; D009039:Motion Perception / Q000502:physiology*; D017711:Nonlinear Dynamics; D011601:Psychophysics