Stroboscopic motion reversals in delay-coupled neural fields

Visual illusions provide a window into the mechanisms underlying visual processing, and dynamical neural circuit models offer a natural framework for proposing and testing theories of their emergence. We propose and analyze a delay-coupled neural field model that explains stroboscopic percepts arising from the subsampling of a moving, often rotating, stimulus, such as the wagon-wheel illusion. Motivated by the role of activity propagation delays in shaping visual percepts, we study neural fields with both uniform and spatially dependent delays, representing the finite time required for signals to travel along axonal projections. Each module is organized as a ring of neurons encoding angular preference, with instantaneous local coupling and delayed long-range coupling strongest between neurons with similar preference. We show that delays generate a family of coexisting traveling bump solutions with distinct, quantized propagation speeds. Using interface-based asymptotic methods, we reduce the neural field dynamics to a low-dimensional system of coupled delay differential equations, enabling a detailed analysis of speed selection, stability, entrainment, and state transitions. Regularly pulsed inputs induce transitions between distinct speed states, including motion opposite to the forcing direction, capturing key features of visual aliasing and stroboscopic motion reversal. These results demonstrate how delayed neural interactions organize perception into discrete dynamical states and provide a mechanistic explanation for stroboscopic visual illusions.