The response curve shown in Figure 3.10 is a plot of a versus
calculated from equation (3.47), the nonlinear phase-amplitude
relation. This curve shows that the string can exhibit
hysteresis near a primary resonance; a slow scan of
the variable (the so-called quasistatic approximation) results in a
sudden jump between the two stable solutions indicated by the solid lines in
Figure 3.10. The jump from the upper branch to the lower branch takes
place at 
. The jump from the lower branch to the upper branch takes
place at 
.
In the parameter regime 
, the response
curve reveals the coexistence of three periodic orbits at the same
frequency, but with different amplitudes.
All these orbits are possible solutions to equation (3.47) for
the values of a indicated in the diagram. All three orbits are harmonic
responses
(or period one orbits) since their
frequency equals the forcing frequency.
The middle solution, indicated by the dashed line in Figure
3.10, is an unstable periodic
orbit.