Motile cells inside living tissues often encounter junctions, where their path branches into several alternative directions of migration. We present a theoretical model of cellular polarization for cells migrating along one-dimensional lines, arriving at a symmetric Y-junction and extending protrusions along the different paths that emanate from the junction. The model predicts the spontaneous emergence of deterministic oscillations between competing protrusions, whereby the cellular

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... n and growth alternates between the competing protrusions. The oscillations are modified by cellular noise, but remain as a dominant feature which affects the time it takes the cell to migrate across the junction. These predicted oscillations in the cellular polarization during the directional decision making process at the junction are found experimentally for two different cell types, noncancerous endothelial and cancerous glioma cells, migrating on patterned network of thin adhesive lanes with junctions.