Characterizing non-autonomous state transitions for the model in Fig 1A.

Schematic representation of the gradient signal implementation in (A) the RD simulations, corresponding to Eq (1), and (B) the one-dimensional projection model, corresponding to Eq (3). (C) Time series of u and the quasi-potential landscape transitions during a transient step-like stimulation for organization in region I (top), III (middle) and IV (bottom) corresponding to Fig 1B (same equations and parameters). Green shaded region: signal interval. Circle/square/triangle: non-polar/polar/transient-polar (memory) state. (D) Exemplary estimate of Gaussian curvature (middle) and corresponding slopes distribution in (x, y) = (uL, uR) direction for each of the identified regions. Slopes distribution around 0 in both direction in conjunction with positive curvature uniquely determines a well (stable steady state) in the potential landscape. Description as in Fig 1F. (TIF)