  Insects use flight muscles attached at the base of the wings to produce
impressive wing flapping frequencies. The maximum power output of these flight
muscles is insufficient to maintain such wing oscillations unless there is good
elastic storage of energy in the insect flight system. Here, we explore the
intrinsic self-oscillatory behavior of an insectile wing model, consisting of
two rigid wings connected at their base by an elastic torsional spring. We
study the wings behavior as a function of the total energy and spring
stiffness. Three types of behavior are identified: end-over-end rotation,
chaotic motion, and periodic flapping. Interestingly, the region of periodic
flapping decreases as energy increases but is favored as stiffness increases.
These findings are consistent with the fact that insect wings and flight
muscles are stiff. They further imply that, by adjusting their muscle stiffness
to the desired energy level, insects can maintain periodic flapping
mechanically for a range of operating conditions.
