Comparison of the stability region in the <i>P–D</i> plane for the control Models 2 and 3.

<p>The horizontal axis is normalized with respect to the critical stiffness (<i>mgh</i>) considering that the intrinsic stiffness is 80% of that value. The stability region of Model 2 is the striped triangle. The stability region of Model 3 is the grey-shaded area, with a gray intensity which is a function of the absolute slope of the Poincaré map: |<i>dF</i>/<i>d</i>θ|_{θ = 0} : the darker the shade the quicker the recovery of upright equilibrium. |<i>dF</i>/<i>d</i>θ|_{θ = 0} = 0 is maximal stability; |<i>dF</i>/<i>d</i>θ|_{θ = 0} = 1 is neutral stability. Dotted areas correspond to instability (|<i>dF</i>/<i>d</i>θ|_{θ = 0}>1). The four panels show how the stability of Model 3 depends upon parameter <i>a</i> which identifies the switching mechanism of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0006169#pone-0006169-g001" target="_blank">Fig. 1</a>. In panels C and D, a small white thin region at the left upper edge of the gray region corresponds to parameter sets in which the equilibrium point is a stable node. Hence in this white region, the Poincaré map cannot be defined though the equilibrium point is stable.