Fig. 3.

Homeostasis increases the robustness of a hair bundle’s frequency selectivity. ($A$ and $B$) Contours of the quality factor $Q$ are shown in the state diagram of model I for homeostasis off $(A)$ and homeostasis on ($B$). Each contour is labeled with its respective value of $Q$, and darker shades of purple indicate larger $Q$ values. ($C$ and $D$) The quality factor along horizontal ($C$) or vertical ($D$) slices that pass through the reference operating points indicated in $A$ and $B$ (white triangle apices) when homeostasis is off (blue) or on (red). ($E-H$) The results for model II are portrayed as for $A-D$. In each contour plot, the Hopf bifurcation curve is colored cyan, and the blue curve marks the boundary of the underdamped region of the state diagram. All parameter values are listed in SI Appendix, Tables S1 and S2, and the alignment of the curves in $C$, $D$, $G$, and $H$ is as described in Fig. 2. Additional bifurcation lines that occur in these regions of the state diagrams are not shown (SI Appendix, sections 8 and 9).