Typical solutions of Model 3 in the phase plane.

<p>In each plane, the initial state at <i>t</i> = 0 is represented by the thick curve segment labeled “1”. This state segment moves in the phase plane according to the DDE of eq. 3 in number order as labeled. A state of the system at time <i>t</i> is represented by the corresponding curve segment whose leading edge is and the tail-end is . The PD controller is turned on and off, respectively, if the tail-end of the segment is located in the on (white) and off (gray-shaded) regions in the phase plane. Dotted lines are the stable manifold (arrow heads directing the equilibrium) and the unstable manifold (arrow heads departing away from the equilibrium). A: A typical orbit of eq. 3 when the proportional gain <i>P</i> of the PD controller is small. B: A typical orbit of eq. 3 when the gain <i>P</i> is large.