Analyses of the core motif with symmetrical parameters. a-c. Phase plane portraits for three values of primary signal strength (zero, intermediate, high), in the absence of polarizing signals (S2 = S3 = 0). Green curve: X nullcline; red curve: Y nullcline; blue arrow: representative vector in the phase space; closed circle: stable steady state; open circle: unstable steady state; gray curve: separatrix. d. One-parameter bifurcation diagram for steady state level of X as a function of primary signal S1. Solid curve: stable steady state; dashed curve: unstable steady state. e. Two-parameter bifurcation diagram with respect to primary signal S1 and polarizing signal S2, with S3 = 0. Solid curve: locus of pitchfork bifurcation points. The pitchfork bifurcation points coalesce and disappear at S2 = 0.357. f. Bidirectional two-parameter bifurcation diagram with respect to primary signal S1 and polarizing signals S2 and S3. Top half: S1—S2 diagram, with S3 = 0, as in panel E. Bottom half: S1—S3 diagram, with S2 = 0. The types of stable steady states in each region are annotated as colored circles. Adjoined circles: multistability. See Figure 1 for interpretation of the color scheme. g. Simulation results for treatment of a population of cells simultaneously with primary and polarizing signals. h. Simulation results for sequential treatment: polarizing signal followed by primary signal. I. Simulation results for sequential treatment: primary signal followed by polarizing signal. In G-I, the heterogeneity scores with respect to XSP and YSP are plotted.